ASVAB Arithmetic Reasoning Practice Test (2026) is a quick way to drill exam-style word problems in a four-choice format. Each item includes the correct answer, a concise explanation, and official citations where applicable so you can verify the underlying rule or testing guidance. Work through the set, note what you miss, review the referenced concept, then retake missed topics until the setups feel automatic.
FAQ
Where can I find ASVAB arithmetic reasoning practice questions?
Use a question set that matches real AR wording: multi-step word problems, ratios, rates, percent change, and basic algebra setups. This page is designed for repetition—answer first, then use “Show Answer” to compare your setup to the explained method.
What do arithmetic reasoning questions on the ASVAB focus on?
They focus on practical math in context: translating words into equations, tracking units, and choosing efficient operations. Expect proportions, averages, fractions/decimals/percents, and rate-time-distance scenarios where the main challenge is building the correct setup.
Is there an ASVAB arithmetic reasoning practice test PDF?
Yes—use your browser’s print-to-PDF feature on this page to save a clean copy for offline work. If you do that, keep the on-page explanations handy for checking your solution steps and confirming the exact reasoning behind the correct option.
How many arithmetic reasoning questions are on the ASVAB?
It varies by test format and form, but Arithmetic Reasoning is a timed subtest with enough items to reward pacing and clean setups. Plan for a few dozen questions and practice moving on when a problem is taking too long, then return if time remains.
What is arithmetic reasoning on the ASVAB?
It’s the subtest that measures your ability to solve word problems using basic arithmetic, fractions, decimals, percents, and simple algebra. The skill is reading carefully, identifying what’s being asked, and translating the situation into a workable equation.
ASVAB Arithmetic Reasoning Practice Test
Q001. A store marks up an item by 35% above cost, then discounts the marked price by 20%. If the cost is $80, what is the sale price?
Correct Answer: A
Explanation: Marked price = 80 × 1.35 = 108. Sale price = 108 × 0.80 = 86.40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change.
Explanation: Marked price = 80 × 1.35 = 108. Sale price = 108 × 0.80 = 86.40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change.
Q002. A recipe uses flour and sugar in a ratio of 5:2 by weight. If 21 ounces of the mix are made, how many ounces of sugar are in the mix?
Correct Answer: B
Explanation: Total parts = 5 + 2 = 7. Sugar is 2 parts, so sugar = (2/7) × 21 = 6 ounces.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios and proportional reasoning.
Explanation: Total parts = 5 + 2 = 7. Sugar is 2 parts, so sugar = (2/7) × 21 = 6 ounces.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios and proportional reasoning.
Q003. A training manual has 64 pages. If 3/8 of the pages are technical diagrams, how many pages are NOT technical diagrams?
Correct Answer: C
Explanation: Technical pages = (3/8) × 64 = 24. Non-technical pages = 64 − 24 = 40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole.
Explanation: Technical pages = (3/8) × 64 = 24. Non-technical pages = 64 − 24 = 40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole.
Q004. A bus travels 180 miles at 60 mph and returns the same 180 miles at 45 mph. What is the average speed for the entire round trip (to the nearest tenth)?
Correct Answer: B
Explanation: Time out = 180/60 = 3 hr. Time back = 180/45 = 4 hr. Total distance = 360 miles, total time = 7 hr, so average speed = 360/7 ≈ 51.4 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed = total distance ÷ total time.
Explanation: Time out = 180/60 = 3 hr. Time back = 180/45 = 4 hr. Total distance = 360 miles, total time = 7 hr, so average speed = 360/7 ≈ 51.4 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed = total distance ÷ total time.
Q005. A 10-liter cleaning solution is 30% concentrate. How many liters of water must be added to make the solution 18% concentrate?
Correct Answer: C
Explanation: Concentrate amount stays the same: 30% of 10 L = 3 L. After adding x liters, 3/(10 + x) = 0.18, so 10 + x = 3/0.18 = 16.666…, and x ≈ 6.7 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture/concentration with invariant amount.
Explanation: Concentrate amount stays the same: 30% of 10 L = 3 L. After adding x liters, 3/(10 + x) = 0.18, so 10 + x = 3/0.18 = 16.666…, and x ≈ 6.7 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture/concentration with invariant amount.
Q006. A worker earns $18 per hour for the first 40 hours and 1.5 times the hourly rate for overtime. If the worker logs 46 hours in a week, what is the total pay?
Correct Answer: C
Explanation: Regular pay = 40 × 18 = 720. Overtime hours = 6, overtime rate = 18 × 1.5 = 27, overtime pay = 6 × 27 = 162. Total = 720 + 162 = 882.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise rates and overtime calculation.
Explanation: Regular pay = 40 × 18 = 720. Overtime hours = 6, overtime rate = 18 × 1.5 = 27, overtime pay = 6 × 27 = 162. Total = 720 + 162 = 882.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise rates and overtime calculation.
Q007. A contractor uses 12 bags of concrete to cover 960 square feet. At the same coverage rate, how many bags are needed to cover 1,500 square feet (round up to a whole bag)?
Correct Answer: B
Explanation: Bags per sq ft = 12/960 = 1/80. Bags for 1,500 sq ft = 1500/80 = 18.75, and you must round up to 19 bags.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate and proportional scaling.
Explanation: Bags per sq ft = 12/960 = 1/80. Bags for 1,500 sq ft = 1500/80 = 18.75, and you must round up to 19 bags.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate and proportional scaling.
Q008. A number is increased by 15% and the result is 69. What was the original number?
Correct Answer: C
Explanation: If x is the original number, then x × 1.15 = 69. So x = 69/1.15 = 60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent change.
Explanation: If x is the original number, then x × 1.15 = 69. So x = 69/1.15 = 60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent change.
Q009. Worker A can complete a job in 10 hours and Worker B can complete the same job in 15 hours. About how long will it take them to complete the job together?
Correct Answer: B
Explanation: Combined rate = 1/10 + 1/15 = (3/30) + (2/30) = 5/30 = 1/6 job per hour, so time = 6 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: work-rate (combined rates).
Explanation: Combined rate = 1/10 + 1/15 = (3/30) + (2/30) = 5/30 = 1/6 job per hour, so time = 6 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: work-rate (combined rates).
Q010. The average of 5 numbers is 18. Four of the numbers are 12, 15, 20, and 25. What is the fifth number?
Correct Answer: B
Explanation: Total for 5 numbers = 5 × 18 = 90. Sum of four numbers = 12 + 15 + 20 + 25 = 72. Fifth = 90 − 72 = 18.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Explanation: Total for 5 numbers = 5 × 18 = 90. Sum of four numbers = 12 + 15 + 20 + 25 = 72. Fifth = 90 − 72 = 18.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Q011. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If 2 marbles are drawn without replacement, what is the probability that both marbles are NOT red?
Correct Answer: B
Explanation: Non-red marbles = 3 + 2 = 5 out of 10. Probability first is non-red = 5/10. Then 4 non-red remain out of 9, so probability = (5/10) × (4/9) = 20/90 = 2/9.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability without replacement.
Explanation: Non-red marbles = 3 + 2 = 5 out of 10. Probability first is non-red = 5/10. Then 4 non-red remain out of 9, so probability = (5/10) × (4/9) = 20/90 = 2/9.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability without replacement.
Q012. A phone plan charges a $25 base fee plus $0.08 per text message. If the total bill is $37.80, how many text messages were sent?
Correct Answer: C
Explanation: Text charges = 37.80 − 25 = 12.80. Texts = 12.80/0.08 = 160.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: linear cost equation.
Explanation: Text charges = 37.80 − 25 = 12.80. Texts = 12.80/0.08 = 160.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: linear cost equation.
Q013. A car uses 12 gallons of fuel to travel 330 miles. At this rate, how many miles per gallon does the car get?
Correct Answer: C
Explanation: Miles per gallon = 330 ÷ 12 = 27.5 mpg.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate.
Explanation: Miles per gallon = 330 ÷ 12 = 27.5 mpg.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate.
Q014. A paycheck has a gross amount of $1,250. If total deductions are 18% of gross pay, what is the net pay?
Correct Answer: A
Explanation: Net pay = gross × (1 − 0.18) = 1250 × 0.82 = 1025.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a quantity.
Explanation: Net pay = gross × (1 − 0.18) = 1250 × 0.82 = 1025.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a quantity.
Q015. A rectangular yard is 30 feet by 18 feet. If a 4-foot-wide gate does not require fencing, how many feet of fencing are needed to enclose the yard?
Correct Answer: B
Explanation: Perimeter = 2(30 + 18) = 96 feet. Subtract the 4-foot gate: 96 − 4 = 92 feet.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: perimeter with adjustment.
Explanation: Perimeter = 2(30 + 18) = 96 feet. Subtract the 4-foot gate: 96 − 4 = 92 feet.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: perimeter with adjustment.
Q016. A store buys pens for $0.60 each and sells them for $0.95 each. If 240 pens are sold, what is the total profit?
Correct Answer: C
Explanation: Profit per pen = 0.95 − 0.60 = 0.35. Total profit = 240 × 0.35 = 84.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit profit × quantity.
Explanation: Profit per pen = 0.95 − 0.60 = 0.35. Total profit = 240 × 0.35 = 84.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit profit × quantity.
Q017. If 3/5 of a fuel tank holds 27 gallons, what is the tank’s full capacity?
Correct Answer: C
Explanation: If (3/5) × capacity = 27, then capacity = 27 ÷ (3/5) = 27 × (5/3) = 45.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving for a whole from a fraction.
Explanation: If (3/5) × capacity = 27, then capacity = 27 ÷ (3/5) = 27 × (5/3) = 45.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving for a whole from a fraction.
Q018. A savings account earns simple interest. If $2,400 is invested at 5.5% annual simple interest for 18 months, how much interest is earned?
Correct Answer: C
Explanation: Time = 18 months = 1.5 years. Simple interest = P × r × t = 2400 × 0.055 × 1.5 = 198.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest.
Explanation: Time = 18 months = 1.5 years. Simple interest = P × r × t = 2400 × 0.055 × 1.5 = 198.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest.
Q019. A class has 28 students. The ratio of girls to boys is 3:4. How many girls are in the class?
Correct Answer: A
Explanation: Total parts = 3 + 4 = 7. Each part = 28/7 = 4. Girls = 3 parts = 3 × 4 = 12.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios to totals.
Explanation: Total parts = 3 + 4 = 7. Each part = 28/7 = 4. Girls = 3 parts = 3 × 4 = 12.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios to totals.
Q020. A printer produces 45 pages in 3 minutes at a steady rate. How long will it take to print 200 pages at the same rate?
Correct Answer: B
Explanation: Rate = 45/3 = 15 pages per minute. Time for 200 pages = 200/15 = 13.333… minutes = 13 minutes 20 seconds.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate and time conversion.
Explanation: Rate = 45/3 = 15 pages per minute. Time for 200 pages = 200/15 = 13.333… minutes = 13 minutes 20 seconds.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate and time conversion.
Q021. A store runs a “buy 2, get 1 half off” deal on $14 items. What is the total cost before tax if you buy 3 items?
Correct Answer: C
Explanation: Two items are full price: 14 + 14 = 28. The third is half off: 14 × 0.5 = 7. Total = 28 + 7 = 35.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: discounts and totals.
Explanation: Two items are full price: 14 + 14 = 28. The third is half off: 14 × 0.5 = 7. Total = 28 + 7 = 35.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: discounts and totals.
Q022. A ladder is 15 feet long and reaches 12 feet up a vertical wall. How far is the base of the ladder from the wall?
Correct Answer: C
Explanation: Using the Pythagorean theorem: base = √(15² − 12²) = √(225 − 144) = √81 = 9 feet.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: right-triangle relationship (Pythagorean theorem).
Explanation: Using the Pythagorean theorem: base = √(15² − 12²) = √(225 − 144) = √81 = 9 feet.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: right-triangle relationship (Pythagorean theorem).
Q023. A test has 50 questions worth 2 points each. A passing score is 80%. How many questions must be answered correctly to pass?
Correct Answer: C
Explanation: Total points = 50 × 2 = 100. To score 80%, you need 80 points. Each correct answer is 2 points, so 80/2 = 40 questions correct.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of total and unit conversion.
Explanation: Total points = 50 × 2 = 100. To score 80%, you need 80 points. Each correct answer is 2 points, so 80/2 = 40 questions correct.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of total and unit conversion.
Q024. A worker’s weekly pay increases from $520 to $598. What is the percent increase?
Correct Answer: B
Explanation: Increase = 598 − 520 = 78. Percent increase = 78/520 = 0.15 = 15%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change.
Explanation: Increase = 598 − 520 = 78. Percent increase = 78/520 = 0.15 = 15%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change.
Q025. A loan is repaid with 24 equal payments of $175. If the original amount borrowed was $3,750, how much interest is paid in total?
Correct Answer: C
Explanation: Total repaid = 24 × 175 = 4,200. Interest paid = 4,200 − 3,750 = 450.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: total cost and interest as difference.
Explanation: Total repaid = 24 × 175 = 4,200. Interest paid = 4,200 − 3,750 = 450.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: total cost and interest as difference.
Q026. A car travels 120 miles in city driving at 24 miles per gallon and 180 miles on the highway at 30 miles per gallon. What is the overall miles per gallon for the entire trip (to the nearest tenth)?
Correct Answer: B
Explanation: City gallons = 120 ÷ 24 = 5. Highway gallons = 180 ÷ 30 = 6. Total miles = 300 and total gallons = 11, so overall mpg = 300 ÷ 11 ≈ 27.3.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average via totals (miles per gallon).
Explanation: City gallons = 120 ÷ 24 = 5. Highway gallons = 180 ÷ 30 = 6. Total miles = 300 and total gallons = 11, so overall mpg = 300 ÷ 11 ≈ 27.3.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average via totals (miles per gallon).
Q027. A fundraiser sells adult tickets for $12 and student tickets for $8. If 185 tickets are sold for a total of $1,860, how many adult tickets were sold?
Correct Answer: C
Explanation: Let a be adult tickets and s be student tickets. a + s = 185 and 12a + 8s = 1860. Substitute s = 185 − a: 12a + 8(185 − a) = 1860 → 4a = 380 → a = 95.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving a system from totals and values.
Explanation: Let a be adult tickets and s be student tickets. a + s = 185 and 12a + 8s = 1860. Substitute s = 185 − a: 12a + 8(185 − a) = 1860 → 4a = 380 → a = 95.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving a system from totals and values.
Q028. You need 50 liters of an 18% saline solution by mixing a 10% solution with a 25% solution. How many liters of the 25% solution are needed (to the nearest tenth)?
Correct Answer: C
Explanation: Let x be liters of 25% and 50 − x be liters of 10%. Salt: 0.25x + 0.10(50 − x) must equal 0.18 × 50 = 9. So 0.15x + 5 = 9 → x = 26.666…, which is 26.7 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture/concentration with conservation of solute.
Explanation: Let x be liters of 25% and 50 − x be liters of 10%. Salt: 0.25x + 0.10(50 − x) must equal 0.18 × 50 = 9. So 0.15x + 5 = 9 → x = 26.666…, which is 26.7 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture/concentration with conservation of solute.
Q029. A shipping box weighs 2.4 lb when empty. Filled with identical parts, the box weighs 18.6 lb. If each part weighs 0.27 lb, how many parts are in the box?
Correct Answer: C
Explanation: Weight of parts only = 18.6 − 2.4 = 16.2 lb. Number of parts = 16.2 ÷ 0.27 = 60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: subtracting a fixed weight and dividing by unit weight.
Explanation: Weight of parts only = 18.6 − 2.4 = 16.2 lb. Number of parts = 16.2 ÷ 0.27 = 60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: subtracting a fixed weight and dividing by unit weight.
Q030. A price increases by 12% and then decreases by 12%. If the original price was $250, what is the final price?
Correct Answer: A
Explanation: After a 12% increase: 250 × 1.12 = 280. After a 12% decrease: 280 × 0.88 = 246.40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change is multiplicative.
Explanation: After a 12% increase: 250 × 1.12 = 280. After a 12% decrease: 280 × 0.88 = 246.40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change is multiplicative.
Q031. Pipe A fills a tank in 6 hours and Pipe B fills the same tank in 8 hours. A drain empties the full tank in 12 hours. If both pipes and the drain are open, how long will it take to fill the tank?
Correct Answer: B
Explanation: Net rate = 1/6 + 1/8 − 1/12. Using a common denominator of 24: 4/24 + 3/24 − 2/24 = 5/24 tank per hour. Time = 1 ÷ (5/24) = 24/5 = 4.8 hours = 4 hours 48 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined work rates with subtraction for loss.
Explanation: Net rate = 1/6 + 1/8 − 1/12. Using a common denominator of 24: 4/24 + 3/24 − 2/24 = 5/24 tank per hour. Time = 1 ÷ (5/24) = 24/5 = 4.8 hours = 4 hours 48 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined work rates with subtraction for loss.
Q032. In a factory, 4% of items are defective. If 3 items are selected at random, what is the probability that none are defective (assume selections are independent)?
Correct Answer: B
Explanation: Probability an item is not defective is 1 − 0.04 = 0.96. Probability all three are not defective is 0.96 × 0.96 × 0.96 = 0.96³ ≈ 0.8847, or about 88.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability of independent events.
Explanation: Probability an item is not defective is 1 − 0.04 = 0.96. Probability all three are not defective is 0.96 × 0.96 × 0.96 = 0.96³ ≈ 0.8847, or about 88.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability of independent events.
Q033. A map uses a scale of 1 inch = 15 miles. Two towns are 3.6 inches apart on the map. About how many miles apart are the towns?
Correct Answer: B
Explanation: Distance = 3.6 × 15 = 54 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion using scale.
Explanation: Distance = 3.6 × 15 = 54 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion using scale.
Q034. A flight departs at 2:35 PM Mountain Time and lasts 3 hours 50 minutes. It lands in Central Time (one hour ahead). What is the local arrival time in Central Time?
Correct Answer: B
Explanation: Add flight time: 2:35 PM + 3:50 = 6:25 PM Mountain Time. Central Time is one hour ahead, so arrival is 7:25 PM Central Time.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: elapsed time plus time-zone adjustment.
Explanation: Add flight time: 2:35 PM + 3:50 = 6:25 PM Mountain Time. Central Time is one hour ahead, so arrival is 7:25 PM Central Time.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: elapsed time plus time-zone adjustment.
Q035. A salesperson earns $420 per week plus 6% commission on weekly sales. If the salesperson’s total pay is $810 for the week, what were the total sales?
Correct Answer: B
Explanation: Commission = 810 − 420 = 390. Since commission is 6% of sales, sales = 390 ÷ 0.06 = 6,500.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent-of-sales commission.
Explanation: Commission = 810 − 420 = 390. Since commission is 6% of sales, sales = 390 ÷ 0.06 = 6,500.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent-of-sales commission.
Q036. A warehouse has 2,400 units in stock. After an audit, 7.5% are found damaged and removed. How many units remain?
Correct Answer: C
Explanation: Damaged units = 2400 × 0.075 = 180. Remaining units = 2400 − 180 = 2220.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a quantity and subtraction.
Explanation: Damaged units = 2400 × 0.075 = 180. Remaining units = 2400 − 180 = 2220.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a quantity and subtraction.
Q037. A 3-pound bag costs $8.25 and a 5-pound bag costs $13.25. Which statement is true about unit price?
Correct Answer: B
Explanation: Unit price for 3 lb = 8.25 ÷ 3 = 2.75 per lb. Unit price for 5 lb = 13.25 ÷ 5 = 2.65 per lb. The 5-pound bag is cheaper by 2.75 − 2.65 = 0.10 per lb.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate comparison.
Explanation: Unit price for 3 lb = 8.25 ÷ 3 = 2.75 per lb. Unit price for 5 lb = 13.25 ÷ 5 = 2.65 per lb. The 5-pound bag is cheaper by 2.75 − 2.65 = 0.10 per lb.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate comparison.
Q038. A recipe uses 3/4 cup of oil to make 8 servings. How much oil is needed to make 14 servings?
Correct Answer: B
Explanation: Scale the amount by 14/8 = 7/4. Oil needed = (3/4) × (7/4) = 21/16 = 1 5/16 cups.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional scaling with fractions.
Explanation: Scale the amount by 14/8 = 7/4. Oil needed = (3/4) × (7/4) = 21/16 = 1 5/16 cups.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional scaling with fractions.
Q039. The average of 6 numbers is 14. After adding a seventh number, the average becomes 15. What is the seventh number?
Correct Answer: C
Explanation: Sum of 6 numbers = 6 × 14 = 84. Sum of 7 numbers = 7 × 15 = 105. Seventh number = 105 − 84 = 21.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Explanation: Sum of 6 numbers = 6 × 14 = 84. Sum of 7 numbers = 7 × 15 = 105. Seventh number = 105 − 84 = 21.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Q040. A rectangular storage bin has a volume of 5.4 cubic feet. It is 1.5 ft high and 2.0 ft wide. What is its length?
Correct Answer: C
Explanation: Volume = length × width × height, so length = 5.4 ÷ (2.0 × 1.5) = 5.4 ÷ 3 = 1.8 ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: volume of a rectangular prism.
Explanation: Volume = length × width × height, so length = 5.4 ÷ (2.0 × 1.5) = 5.4 ÷ 3 = 1.8 ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: volume of a rectangular prism.
Q041. A contractor must cover a 48-foot run using boards that are 8 feet long. Because of cuts, 6 inches of each board is wasted. How many boards are needed?
Correct Answer: B
Explanation: Each board effectively covers 8.0 − 0.5 = 7.5 feet. Boards needed = 48 ÷ 7.5 = 6.4, so you must round up to 7 boards.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion (inches to feet) and rounding up.
Explanation: Each board effectively covers 8.0 − 0.5 = 7.5 feet. Boards needed = 48 ÷ 7.5 = 6.4, so you must round up to 7 boards.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion (inches to feet) and rounding up.
Q042. Machine A makes 120 bolts per hour and Machine B makes 90 bolts per hour. They run together for 5 hours, and 6% of the bolts are rejected. How many acceptable bolts are produced?
Correct Answer: B
Explanation: Total bolts made = (120 + 90) × 5 = 210 × 5 = 1050. Acceptable bolts = 94% of 1050 = 0.94 × 1050 = 987.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined production rates and percent reduction.
Explanation: Total bolts made = (120 + 90) × 5 = 210 × 5 = 1050. Acceptable bolts = 94% of 1050 = 0.94 × 1050 = 987.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined production rates and percent reduction.
Q043. An account earns simple interest. If $3,200 is invested at 4.25% per year for 9 months, how much interest is earned?
Correct Answer: B
Explanation: Time = 9 months = 0.75 years. Interest = P × r × t = 3200 × 0.0425 × 0.75 = 102.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest.
Explanation: Time = 9 months = 0.75 years. Interest = P × r × t = 3200 × 0.0425 × 0.75 = 102.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest.
Q044. In a unit, the ratio of officers to enlisted personnel is 3:17. If there are 180 total personnel, how many officers are there?
Correct Answer: B
Explanation: Total parts = 3 + 17 = 20. Each part = 180 ÷ 20 = 9. Officers = 3 parts = 3 × 9 = 27.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios to totals.
Explanation: Total parts = 3 + 17 = 20. Each part = 180 ÷ 20 = 9. Officers = 3 parts = 3 × 9 = 27.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios to totals.
Q045. A laptop costs $920. The store takes 10% off the price, then offers a $50 mail-in rebate. What is the final cost after the rebate (before tax)?
Correct Answer: A
Explanation: After 10% off: 920 × 0.90 = 828. After the $50 rebate: 828 − 50 = 778.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount followed by subtraction.
Explanation: After 10% off: 920 × 0.90 = 828. After the $50 rebate: 828 − 50 = 778.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount followed by subtraction.
Q046. A driver logs 48 miles on Monday, 52 on Tuesday, 0 on Wednesday, 64 on Thursday, and 56 on Friday. How many miles must the driver travel on Saturday to make the 6-day average 55 miles per day?
Correct Answer: C
Explanation: To average 55 miles over 6 days, total miles must be 6 × 55 = 330. Current total is 48 + 52 + 0 + 64 + 56 = 220. Saturday miles needed = 330 − 220 = 110.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: target average using total required.
Explanation: To average 55 miles over 6 days, total miles must be 6 × 55 = 330. Current total is 48 + 52 + 0 + 64 + 56 = 220. Saturday miles needed = 330 − 220 = 110.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: target average using total required.
Q047. A gym membership costs $39 per month. If you pay quarterly, the gym discounts the total 3-month cost by 8%. What is the quarterly price?
Correct Answer: A
Explanation: Three months at full price is 3 × 39 = 117. Apply the 8% discount: 117 × 0.92 = 107.64.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount on a total.
Explanation: Three months at full price is 3 × 39 = 117. Apply the 8% discount: 117 × 0.92 = 107.64.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount on a total.
Q048. A boat travels 24 miles downstream in 2 hours and returns upstream the same 24 miles in 3 hours. What is the speed of the current?
Correct Answer: B
Explanation: Downstream speed = 24 ÷ 2 = 12 mph and upstream speed = 24 ÷ 3 = 8 mph. Let b be boat speed in still water and c be current: b + c = 12 and b − c = 8. Solving gives c = 2 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate problems with opposite directions.
Explanation: Downstream speed = 24 ÷ 2 = 12 mph and upstream speed = 24 ÷ 3 = 8 mph. Let b be boat speed in still water and c be current: b + c = 12 and b − c = 8. Solving gives c = 2 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate problems with opposite directions.
Q049. A jar contains 60 coins worth $4.35 total, made up of nickels and dimes only. How many dimes are in the jar?
Correct Answer: B
Explanation: Let d be dimes and n be nickels. d + n = 60 and 10d + 5n = 435 cents. Divide by 5: 2d + n = 87. Subtract (d + n = 60) to get d = 27.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: system of equations from counts and values.
Explanation: Let d be dimes and n be nickels. d + n = 60 and 10d + 5n = 435 cents. Divide by 5: 2d + n = 87. Subtract (d + n = 60) to get d = 27.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: system of equations from counts and values.
Q050. A job requires 40.5 cubic yards of concrete. Each truck carries 2.25 cubic yards per trip. How many total truck trips are needed to deliver all the concrete?
Correct Answer: B
Explanation: Total trips = 40.5 ÷ 2.25 = 18, because 2.25 × 18 = 40.5.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: dividing a total by capacity (unit rate).
Explanation: Total trips = 40.5 ÷ 2.25 = 18, because 2.25 × 18 = 40.5.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: dividing a total by capacity (unit rate).
Q051. A $180 item has a 15% coupon applied, then 6.5% sales tax is charged on the discounted price. What is the final price (rounded to the nearest cent)?
Correct Answer: B
Explanation: Discounted price = 180 × 0.85 = 153. Tax = 153 × 0.065 = 9.945, so total = 153 + 9.945 = 162.945, which rounds to $162.95.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change with tax.
Explanation: Discounted price = 180 × 0.85 = 153. Tax = 153 × 0.065 = 9.945, so total = 153 + 9.945 = 162.945, which rounds to $162.95.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change with tax.
Q052. Paint A and Paint B are mixed in a 3:5 ratio. If 32 gallons of the mixture are made, how many gallons are Paint B?
Correct Answer: C
Explanation: Total parts = 3 + 5 = 8. Paint B is 5 parts, so B = (5/8) × 32 = 20 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios and proportional parts.
Explanation: Total parts = 3 + 5 = 8. Paint B is 5 parts, so B = (5/8) × 32 = 20 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios and proportional parts.
Q053. A truck drives 150 miles at 50 mph, rests for 30 minutes, then drives 120 miles at 60 mph. What is the average speed for the entire trip including the rest (to the nearest tenth)?
Correct Answer: B
Explanation: Time 1 = 150/50 = 3 hours. Rest = 0.5 hour. Time 2 = 120/60 = 2 hours. Total distance = 270 miles and total time = 5.5 hours, so average speed = 270/5.5 ≈ 49.1 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed = total distance ÷ total time.
Explanation: Time 1 = 150/50 = 3 hours. Rest = 0.5 hour. Time 2 = 120/60 = 2 hours. Total distance = 270 miles and total time = 5.5 hours, so average speed = 270/5.5 ≈ 49.1 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed = total distance ÷ total time.
Q054. A tank holds 18 gallons. A leak drains 2 quarts per hour. About how many hours will it take to empty the tank?
Correct Answer: C
Explanation: Convert gallons to quarts: 18 gallons = 18 × 4 = 72 quarts. At 2 quarts per hour, time = 72/2 = 36 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion and rate.
Explanation: Convert gallons to quarts: 18 gallons = 18 × 4 = 72 quarts. At 2 quarts per hour, time = 72/2 = 36 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion and rate.
Q055. A device sells for $500. If the company wants a 30% gross margin based on the selling price, what is the maximum cost the company can pay for the device?
Correct Answer: C
Explanation: Gross margin of 30% means cost is 70% of selling price. Cost = 500 × 0.70 = 350.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a base (margin on selling price).
Explanation: Gross margin of 30% means cost is 70% of selling price. Cost = 500 × 0.70 = 350.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a base (margin on selling price).
Q056. A fair coin is flipped 3 times. What is the probability of getting at least one head?
Correct Answer: D
Explanation: Use the complement: probability of no heads (all tails) is (1/2)³ = 1/8. So probability of at least one head is 1 − 1/8 = 7/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: complement probability.
Explanation: Use the complement: probability of no heads (all tails) is (1/2)³ = 1/8. So probability of at least one head is 1 − 1/8 = 7/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: complement probability.
Q057. A 20 ft by 14 ft garden is surrounded by a 1-ft-wide path on the outside. What is the area of the path?
Correct Answer: B
Explanation: Outer dimensions are (20 + 2) by (14 + 2) = 22 by 16, so outer area = 352. Garden area = 20 × 14 = 280. Path area = 352 − 280 = 72 sq ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area difference using expanded dimensions.
Explanation: Outer dimensions are (20 + 2) by (14 + 2) = 22 by 16, so outer area = 352. Garden area = 20 × 14 = 280. Path area = 352 − 280 = 72 sq ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area difference using expanded dimensions.
Q058. A service charges a flat $3 fee to exchange money. After the fee, each unit of foreign currency costs $1.25. If you start with $90, how many units can you buy (to the nearest tenth)?
Correct Answer: A
Explanation: Money available after fee = 90 − 3 = 87. Units = 87/1.25 = 69.6 units.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: subtract fixed fee and divide by unit rate.
Explanation: Money available after fee = 90 − 3 = 87. Units = 87/1.25 = 69.6 units.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: subtract fixed fee and divide by unit rate.
Q059. A course grade is 30% homework, 50% tests, and 20% final exam. A student has an 84 homework average, 76 test average, and a 90 on the final. What is the overall course average?
Correct Answer: C
Explanation: Weighted average = 0.30(84) + 0.50(76) + 0.20(90) = 25.2 + 38 + 18 = 81.2.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average.
Explanation: Weighted average = 0.30(84) + 0.50(76) + 0.20(90) = 25.2 + 38 + 18 = 81.2.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average.
Q060. A worker can complete a job in 9 hours of work time. The worker works 3 hours, takes a 45-minute break, then finishes the job at the same pace. How long is it from start to finish?
Correct Answer: C
Explanation: After 3 hours, 6 hours of work remain. Total elapsed time = 3 hours + 0.75 hour break + 6 hours = 9.75 hours = 9 hours 45 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: separating working time from elapsed time.
Explanation: After 3 hours, 6 hours of work remain. Total elapsed time = 3 hours + 0.75 hour break + 6 hours = 9.75 hours = 9 hours 45 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: separating working time from elapsed time.
Q061. A 40-liter solution is 15% alcohol. How many liters of pure alcohol must be added to make the solution 20% alcohol?
Correct Answer: B
Explanation: Initial alcohol = 0.15 × 40 = 6 L. Add x liters of pure alcohol: (6 + x)/(40 + x) = 0.20. Solve: 6 + x = 8 + 0.2x → 0.8x = 2 → x = 2.5 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture/concentration with conserved component.
Explanation: Initial alcohol = 0.15 × 40 = 6 L. Add x liters of pure alcohol: (6 + x)/(40 + x) = 0.20. Solve: 6 + x = 8 + 0.2x → 0.8x = 2 → x = 2.5 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture/concentration with conserved component.
Q062. $1,800 is invested at 6% annual simple interest for 14 months. How much interest is earned?
Correct Answer: C
Explanation: Time = 14/12 = 1.1666… years. Interest = 1800 × 0.06 × 1.1666… = 1800 × 0.07 = 126.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (I = Prt).
Explanation: Time = 14/12 = 1.1666… years. Interest = 1800 × 0.06 × 1.1666… = 1800 × 0.07 = 126.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (I = Prt).
Q063. A recipe uses 250 g of pasta for 4 servings. How many grams are needed for 11 servings?
Correct Answer: C
Explanation: Scale by 11/4. Pasta needed = 250 × (11/4) = 250 × 2.75 = 687.5 g.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional scaling.
Explanation: Scale by 11/4. Pasta needed = 250 × (11/4) = 250 × 2.75 = 687.5 g.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional scaling.
Q064. Three consecutive integers have a sum of 93. What is the largest integer?
Correct Answer: C
Explanation: The middle integer is 93/3 = 31, so the numbers are 30, 31, and 32. The largest is 32.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: consecutive integers and averages.
Explanation: The middle integer is 93/3 = 31, so the numbers are 30, 31, and 32. The largest is 32.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: consecutive integers and averages.
Q065. Adult tickets cost $13 and child tickets cost $9. If 146 tickets are sold for a total of $1,602, how many adult tickets were sold?
Correct Answer: B
Explanation: Let a be adult and c be child. a + c = 146 and 13a + 9c = 1602. Substitute c = 146 − a: 13a + 9(146 − a) = 1602 → 4a = 288 → a = 72.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: system of equations from totals.
Explanation: Let a be adult and c be child. a + c = 146 and 13a + 9c = 1602. Substitute c = 146 − a: 13a + 9(146 − a) = 1602 → 4a = 288 → a = 72.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: system of equations from totals.
Q066. A package costs $5 plus $1.20 per pound for the first 10 pounds and $0.80 per pound for each pound over 10. What is the shipping cost for an 18-pound package?
Correct Answer: C
Explanation: Cost = 5 + 1.20(10) + 0.80(8) = 5 + 12 + 6.4 = 23.4.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise linear cost.
Explanation: Cost = 5 + 1.20(10) + 0.80(8) = 5 + 12 + 6.4 = 23.4.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise linear cost.
Q067. A generator uses 0.8 gallons per hour while running. It runs for 3.5 hours, then idles for 40 minutes using half the running rate. About how many gallons of fuel are used (to the nearest hundredth)?
Correct Answer: B
Explanation: Running fuel = 3.5 × 0.8 = 2.8 gallons. Idle time = 40/60 = 2/3 hour at 0.4 gal/hr, so idle fuel = (2/3) × 0.4 ≈ 0.2667. Total ≈ 2.8 + 0.2667 = 3.07 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rates with time conversion and scaling.
Explanation: Running fuel = 3.5 × 0.8 = 2.8 gallons. Idle time = 40/60 = 2/3 hour at 0.4 gal/hr, so idle fuel = (2/3) × 0.4 ≈ 0.2667. Total ≈ 2.8 + 0.2667 = 3.07 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rates with time conversion and scaling.
Q068. Which fraction is equal to 0.375 in simplest form?
Correct Answer: A
Explanation: 0.375 = 375/1000. Divide numerator and denominator by 125 to simplify: 375/1000 = 3/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting decimals to simplified fractions.
Explanation: 0.375 = 375/1000. Divide numerator and denominator by 125 to simplify: 375/1000 = 3/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting decimals to simplified fractions.
Q069. A circular track has a radius of 70 meters. About how many meters does a runner travel in 3 full laps (round to the nearest meter)?
Correct Answer: B
Explanation: One lap distance = 2πr = 2π(70) = 140π. Three laps = 420π ≈ 1319.5 meters, which rounds to 1,320 meters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: circumference and scaling by laps.
Explanation: One lap distance = 2πr = 2π(70) = 140π. Three laps = 420π ≈ 1319.5 meters, which rounds to 1,320 meters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: circumference and scaling by laps.
Q070. The average of 6 numbers is 12. After a seventh number is added, the average becomes 13. What is the seventh number?
Correct Answer: B
Explanation: Sum of 6 numbers = 6 × 12 = 72. Sum of 7 numbers = 7 × 13 = 91. Seventh number = 91 − 72 = 19.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Explanation: Sum of 6 numbers = 6 × 12 = 72. Sum of 7 numbers = 7 × 13 = 91. Seventh number = 91 − 72 = 19.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Q071. A town’s population increases by 8% one year and then by 5% the next year. What is the total percent increase over the two years?
Correct Answer: B
Explanation: Successive increases multiply: 1.08 × 1.05 = 1.134. Total increase = 1.134 − 1 = 0.134 = 13.4%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compound percent change.
Explanation: Successive increases multiply: 1.08 × 1.05 = 1.134. Total increase = 1.134 − 1 = 0.134 = 13.4%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compound percent change.
Q072. A monthly budget is $2,400. Housing is 35% of the budget, transportation is 12%, and food is $420. How much money is left for everything else?
Correct Answer: C
Explanation: Housing = 0.35 × 2400 = 840. Transportation = 0.12 × 2400 = 288. Total spent = 840 + 288 + 420 = 1548. Remaining = 2400 − 1548 = 852.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent allocation and remainder.
Explanation: Housing = 0.35 × 2400 = 840. Transportation = 0.12 × 2400 = 288. Total spent = 840 + 288 + 420 = 1548. Remaining = 2400 − 1548 = 852.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent allocation and remainder.
Q073. A tank holds 96 cubic feet when full and is currently 5/8 full. How many cubic feet are needed to fill the tank completely?
Correct Answer: C
Explanation: Remaining fraction = 1 − 5/8 = 3/8. Remaining volume = (3/8) × 96 = 36 cubic feet.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole.
Explanation: Remaining fraction = 1 − 5/8 = 3/8. Remaining volume = (3/8) × 96 = 36 cubic feet.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole.
Q074. A person reads 18 pages in 12 minutes at a steady rate. About how many minutes will it take to read 250 pages at the same rate (to the nearest tenth)?
Correct Answer: B
Explanation: Rate = 18/12 = 1.5 pages per minute. Time = 250/1.5 = 166.666…, which is 166.7 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate and time calculation.
Explanation: Rate = 18/12 = 1.5 pages per minute. Time = 250/1.5 = 166.666…, which is 166.7 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate and time calculation.
Q075. A meal contains 720 calories. If 25% of the calories come from protein and 30% come from fat, how many calories come from carbohydrates?
Correct Answer: C
Explanation: Protein + fat = 25% + 30% = 55%, so carbohydrates are 45%. Carbohydrate calories = 0.45 × 720 = 324.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent remainder of a total.
Explanation: Protein + fat = 25% + 30% = 55%, so carbohydrates are 45%. Carbohydrate calories = 0.45 × 720 = 324.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent remainder of a total.
Q076. A salary is $52,000. It increases by 4%, and then a one-time $1,200 bonus is added. What is the new total annual amount including the bonus?
Correct Answer: C
Explanation: After a 4% raise: 52,000 × 1.04 = 54,080. Add the bonus: 54,080 + 1,200 = 55,280.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase plus fixed addition.
Explanation: After a 4% raise: 52,000 × 1.04 = 54,080. Add the bonus: 54,080 + 1,200 = 55,280.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase plus fixed addition.
Q077. A container holds 18 liters when full. If 2/3 of the contents are used and then 4 liters are added, how many liters are in the container now?
Correct Answer: B
Explanation: Used amount = (2/3) × 18 = 12 liters, leaving 6 liters. After adding 4 liters, total is 10 liters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction used and addition.
Explanation: Used amount = (2/3) × 18 = 12 liters, leaving 6 liters. After adding 4 liters, total is 10 liters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction used and addition.
Q078. After a 22% price decrease, an item costs $390. What was the original price?
Correct Answer: C
Explanation: A 22% decrease means the new price is 78% of original: 0.78 × original = 390. Original = 390/0.78 = 500.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent change.
Explanation: A 22% decrease means the new price is 78% of original: 0.78 × original = 390. Original = 390/0.78 = 500.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent change.
Q079. Worker A can finish a job in 12 hours, Worker B in 18 hours, and Worker C in 9 hours. About how long will they take together to finish the job?
Correct Answer: B
Explanation: Combined rate = 1/12 + 1/18 + 1/9. Using denominator 36: 3/36 + 2/36 + 4/36 = 9/36 = 1/4 job per hour, so time = 4 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined work rates.
Explanation: Combined rate = 1/12 + 1/18 + 1/9. Using denominator 36: 3/36 + 2/36 + 4/36 = 9/36 = 1/4 job per hour, so time = 4 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined work rates.
Q080. Nails cost $0.09 each, but a box of 500 costs $38. If you need 1,200 nails, what is the lowest total cost?
Correct Answer: B
Explanation: Buy 2 boxes for 1,000 nails: 2 × 38 = 76. Buy the remaining 200 nails individually: 200 × 0.09 = 18. Total = 76 + 18 = 94.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compare purchasing options using totals.
Explanation: Buy 2 boxes for 1,000 nails: 2 × 38 = 76. Buy the remaining 200 nails individually: 200 × 0.09 = 18. Total = 76 + 18 = 94.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compare purchasing options using totals.
Q081. A 15-pound coffee blend is 40% dark beans. How many pounds of light beans (0% dark) must be added to make the blend 25% dark?
Correct Answer: C
Explanation: Dark beans amount stays 0.40 × 15 = 6 lb. After adding x lb, 6/(15 + x) = 0.25, so 15 + x = 24 and x = 9 lb.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture with fixed component and changing total.
Explanation: Dark beans amount stays 0.40 × 15 = 6 lb. After adding x lb, 6/(15 + x) = 0.25, so 15 + x = 24 and x = 9 lb.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture with fixed component and changing total.
Q082. A bag has 4 red and 6 blue marbles. Two marbles are drawn with replacement. What is the probability that both marbles are the same color?
Correct Answer: C
Explanation: P(RR) = (4/10)² = 0.16 and P(BB) = (6/10)² = 0.36. Add them: 0.16 + 0.36 = 0.52.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability with replacement and addition of cases.
Explanation: P(RR) = (4/10)² = 0.16 and P(BB) = (6/10)² = 0.36. Add them: 0.16 + 0.36 = 0.52.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability with replacement and addition of cases.
Q083. A machine part length starts at 2.60 cm and increases by 0.15 cm for each next part. What is the length of the 10th part?
Correct Answer: B
Explanation: This is an arithmetic sequence: 10th length = 2.60 + 9(0.15) = 2.60 + 1.35 = 3.95 cm.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: arithmetic sequence (repeated addition).
Explanation: This is an arithmetic sequence: 10th length = 2.60 + 9(0.15) = 2.60 + 1.35 = 3.95 cm.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: arithmetic sequence (repeated addition).
Q084. An item costs $64. A $10 store coupon is applied, then 7% sales tax is added. What is the final price (nearest cent)?
Correct Answer: B
Explanation: Discounted price = 64 − 10 = 54. Tax = 54 × 0.07 = 3.78. Total = 54 + 3.78 = 57.78.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: subtract fixed discount, then apply tax percent.
Explanation: Discounted price = 64 − 10 = 54. Tax = 54 × 0.07 = 3.78. Total = 54 + 3.78 = 57.78.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: subtract fixed discount, then apply tax percent.
Q085. A pipe fills a tank in 5 hours. A drain empties the full tank in 20 hours. If both are open, how long will it take to fill the empty tank?
Correct Answer: C
Explanation: Net rate = 1/5 − 1/20 = 4/20 − 1/20 = 3/20 tank per hour. Time = 1 ÷ (3/20) = 20/3 hours = 6.666… hours = 6 hours 40 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined rates with subtraction.
Explanation: Net rate = 1/5 − 1/20 = 4/20 − 1/20 = 3/20 tank per hour. Time = 1 ÷ (3/20) = 20/3 hours = 6.666… hours = 6 hours 40 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined rates with subtraction.
Q086. A floor plan uses a scale of 1 cm = 4 m. A rectangular room measures 6.5 cm by 4.0 cm on the plan. What is the actual area of the room?
Correct Answer: C
Explanation: Actual dimensions: 6.5 cm → 26 m and 4.0 cm → 16 m. Area = 26 × 16 = 416 m².
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: scale conversion and area.
Explanation: Actual dimensions: 6.5 cm → 26 m and 4.0 cm → 16 m. Area = 26 × 16 = 416 m².
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: scale conversion and area.
Q087. A factory produces 2,000 items. If 8% are defective and 75% of the defective items can be successfully reworked, how many usable items are available after rework?
Correct Answer: C
Explanation: Defective items = 0.08 × 2000 = 160. Initially good items = 2000 − 160 = 1840. Reworked successfully = 0.75 × 160 = 120. Total usable = 1840 + 120 = 1960.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent defective and recovery rate.
Explanation: Defective items = 0.08 × 2000 = 160. Initially good items = 2000 − 160 = 1840. Reworked successfully = 0.75 × 160 = 120. Total usable = 1840 + 120 = 1960.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent defective and recovery rate.
Q088. A server earns $5.50 per hour for an 8-hour shift and makes $180 in tips. If the server must tip-out 12% of tips, what is the total take-home pay?
Correct Answer: B
Explanation: Wages = 5.50 × 8 = 44. Tips kept = 180 × (1 − 0.12) = 180 × 0.88 = 158.40. Total take-home = 44 + 158.40 = 202.40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent reduction and addition.
Explanation: Wages = 5.50 × 8 = 44. Tips kept = 180 × (1 − 0.12) = 180 × 0.88 = 158.40. Total take-home = 44 + 158.40 = 202.40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent reduction and addition.
Q089. A rectangular box is 12 in long, 8 in wide, and 6 in high. Paint covers 120 square inches per ounce. How many ounces are needed to paint the top and all four sides (not the bottom)?
Correct Answer: B
Explanation: Area to paint = top + 4 sides. Top = 12 × 8 = 96. Two long sides: 2(12 × 6) = 144. Two short sides: 2(8 × 6) = 96. Total = 96 + 144 + 96 = 336 sq in. Ounces = 336/120 = 2.8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: surface area and coverage rate.
Explanation: Area to paint = top + 4 sides. Top = 12 × 8 = 96. Two long sides: 2(12 × 6) = 144. Two short sides: 2(8 × 6) = 96. Total = 96 + 144 + 96 = 336 sq in. Ounces = 336/120 = 2.8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: surface area and coverage rate.
Q090. A gas tank holds 16 gallons and is 1/4 full. If 10 gallons are added, what fraction of the tank is full?
Correct Answer: B
Explanation: 1/4 of 16 is 4 gallons. After adding 10, there are 14 gallons. Fraction full = 14/16 = 7/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fractions of a whole and simplification.
Explanation: 1/4 of 16 is 4 gallons. After adding 10, there are 14 gallons. Fraction full = 14/16 = 7/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fractions of a whole and simplification.
Q091. A rectangle is 9 ft by 12 ft. What is the length of its diagonal?
Correct Answer: C
Explanation: Use the Pythagorean theorem: diagonal = √(9² + 12²) = √(81 + 144) = √225 = 15.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: right-triangle relationship (Pythagorean theorem).
Explanation: Use the Pythagorean theorem: diagonal = √(9² + 12²) = √(81 + 144) = √225 = 15.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: right-triangle relationship (Pythagorean theorem).
Q092. Two numbers have a sum of 84. The larger number is 2 times the smaller number plus 6. What is the larger number?
Correct Answer: C
Explanation: Let s be the smaller number and L be the larger. L = 2s + 6 and s + L = 84. Then s + 2s + 6 = 84 → 3s = 78 → s = 26, so L = 2(26) + 6 = 58.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: translating words to equations.
Explanation: Let s be the smaller number and L be the larger. L = 2s + 6 and s + L = 84. Then s + 2s + 6 = 84 → 3s = 78 → s = 26, so L = 2(26) + 6 = 58.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: translating words to equations.
Q093. Five pounds of chicken cost $17.85. At the same unit price, what is the cost of 3.2 pounds (nearest cent)?
Correct Answer: B
Explanation: Unit price = 17.85/5 = 3.57 per pound. Cost for 3.2 lb = 3.57 × 3.2 = 11.424, which rounds to $11.42.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate and multiplication.
Explanation: Unit price = 17.85/5 = 3.57 per pound. Cost for 3.2 lb = 3.57 × 3.2 = 11.424, which rounds to $11.42.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate and multiplication.
Q094. A chemical mixture has 80 liters total. If 35% is Chemical X, how many liters are Chemical X?
Correct Answer: C
Explanation: Chemical X amount = 0.35 × 80 = 28 liters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a quantity.
Explanation: Chemical X amount = 0.35 × 80 = 28 liters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a quantity.
Q095. Eight test scores have an average of 76. After removing two scores, the remaining six scores have an average of 79. What is the average of the two removed scores?
Correct Answer: B
Explanation: Total of 8 scores = 8 × 76 = 608. Total of remaining 6 scores = 6 × 79 = 474. Removed total = 608 − 474 = 134. Average of removed scores = 134/2 = 67.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and difference of totals.
Explanation: Total of 8 scores = 8 × 76 = 608. Total of remaining 6 scores = 6 × 79 = 474. Removed total = 608 − 474 = 134. Average of removed scores = 134/2 = 67.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and difference of totals.
Q096. An item costs $160. It is discounted 25% and then discounted an additional 10% off the new price. What is the final price?
Correct Answer: A
Explanation: After 25% off: 160 × 0.75 = 120. After another 10% off: 120 × 0.90 = 108.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive discounts are multiplicative.
Explanation: After 25% off: 160 × 0.75 = 120. After another 10% off: 120 × 0.90 = 108.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive discounts are multiplicative.
Q097. A traveler leaves at 9:20 AM, travels 2 hours 35 minutes, has a 50-minute layover, then travels 1 hour 45 minutes. What is the arrival time?
Correct Answer: C
Explanation: Total elapsed time = 2:35 + 0:50 + 1:45 = 5:10. Add to 9:20 AM to get 2:30 PM.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: elapsed time addition.
Explanation: Total elapsed time = 2:35 + 0:50 + 1:45 = 5:10. Add to 9:20 AM to get 2:30 PM.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: elapsed time addition.
Q098. A device battery drains 6% per hour when active and 2% per hour in standby. Starting at 100%, it is active for 9 hours and in standby for 5 hours. What percent battery remains?
Correct Answer: B
Explanation: Active drain = 9 × 6% = 54%. Standby drain = 5 × 2% = 10%. Total drain = 64%, so remaining battery = 100% − 64% = 36%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate of change with different phases.
Explanation: Active drain = 9 × 6% = 54%. Standby drain = 5 × 2% = 10%. Total drain = 64%, so remaining battery = 100% − 64% = 36%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate of change with different phases.
Q099. A 12-ounce cereal box is 30% larger than the standard size. What is the standard size (to the nearest hundredth of an ounce)?
Correct Answer: B
Explanation: 12 oz equals 130% of standard: 1.30 × standard = 12. Standard = 12/1.30 ≈ 9.2308, which rounds to 9.23 oz.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent using division.
Explanation: 12 oz equals 130% of standard: 1.30 × standard = 12. Standard = 12/1.30 ≈ 9.2308, which rounds to 9.23 oz.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent using division.
Q100. Alloy A is 60% copper and Alloy B is 35% copper. How many kilograms of Alloy A are needed to make 100 kg of a 50% copper mixture?
Correct Answer: C
Explanation: Let x be kg of Alloy A and 100 − x be kg of Alloy B. Copper: 0.60x + 0.35(100 − x) = 50. Solve: 0.60x + 35 − 0.35x = 50 → 0.25x = 15 → x = 60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture equation with weighted percentages.
Explanation: Let x be kg of Alloy A and 100 − x be kg of Alloy B. Copper: 0.60x + 0.35(100 − x) = 50. Solve: 0.60x + 35 − 0.35x = 50 → 0.25x = 15 → x = 60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture equation with weighted percentages.
Q101. A company buys 75 tablets at $148 each. Shipping is a flat $240, and a bulk discount of 6% applies to the tablet total (not to shipping). What is the final total cost?
Correct Answer: B
Explanation: Tablet total = 75 × 148 = 11,100. Apply 6% discount: 11,100 × 0.94 = 10,434. Add shipping: 10,434 + 240 = 10,674.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount on subtotal plus fixed fee.
Explanation: Tablet total = 75 × 148 = 11,100. Apply 6% discount: 11,100 × 0.94 = 10,434. Add shipping: 10,434 + 240 = 10,674.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount on subtotal plus fixed fee.
Q102. A 9-mile section of trail is mapped as 3.6 inches. Using the same scale, how many inches represent 12.5 miles?
Correct Answer: B
Explanation: Scale = 3.6/9 = 0.4 inches per mile. For 12.5 miles: 12.5 × 0.4 = 5.0 inches.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: scale and proportional reasoning.
Explanation: Scale = 3.6/9 = 0.4 inches per mile. For 12.5 miles: 12.5 × 0.4 = 5.0 inches.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: scale and proportional reasoning.
Q103. A store sells 3-liter bottles of water for $4.50 each or a 12-liter case for $16.20. If you need 36 liters, what is the least cost?
Correct Answer: A
Explanation: Three 12-liter cases give 36 liters. Cost = 3 × 16.20 = 48.60. Buying 3-liter bottles would require 12 bottles: 12 × 4.50 = 54.00, which is higher.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compare purchasing options using totals.
Explanation: Three 12-liter cases give 36 liters. Cost = 3 × 16.20 = 48.60. Buying 3-liter bottles would require 12 bottles: 12 × 4.50 = 54.00, which is higher.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compare purchasing options using totals.
Q104. A worker is paid $19 per hour for the first 40 hours and double time for hours over 40. If the worker earns $1,026 in a week, how many hours were worked?
Correct Answer: B
Explanation: Regular pay = 40 × 19 = 760. Remaining pay = 1,026 − 760 = 266. Overtime rate = 2 × 19 = 38. Overtime hours = 266/38 = 7. Total hours = 40 + 7 = 47.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise pay rates and solving for hours.
Explanation: Regular pay = 40 × 19 = 760. Remaining pay = 1,026 − 760 = 266. Overtime rate = 2 × 19 = 38. Overtime hours = 266/38 = 7. Total hours = 40 + 7 = 47.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise pay rates and solving for hours.
Q105. A 60-gallon tank is 35% full. How many gallons must be added to make it 80% full?
Correct Answer: B
Explanation: Current amount = 0.35 × 60 = 21 gallons. Target amount = 0.80 × 60 = 48 gallons. Amount to add = 48 − 21 = 27 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a whole and difference.
Explanation: Current amount = 0.35 × 60 = 21 gallons. Target amount = 0.80 × 60 = 48 gallons. Amount to add = 48 − 21 = 27 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a whole and difference.
Q106. A bag contains 7 white balls and 5 black balls. Two balls are drawn without replacement. What is the probability both balls are black?
Correct Answer: C
Explanation: Probability first is black = 5/12. Then 4 black remain out of 11, so probability = (5/12) × (4/11) = 20/132 = 5/33.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability without replacement.
Explanation: Probability first is black = 5/12. Then 4 black remain out of 11, so probability = (5/12) × (4/11) = 20/132 = 5/33.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability without replacement.
Q107. A bus fare is $2.40 per ride. A monthly pass costs $54 and covers unlimited rides. For a 30-day month, what is the minimum number of rides needed for the pass to be cheaper?
Correct Answer: C
Explanation: Set 2.40r > 54 for the pass to be cheaper than paying per ride. r > 54/2.40 = 22.5, so at 23 rides the pass becomes cheaper.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: break-even analysis with unit cost.
Explanation: Set 2.40r > 54 for the pass to be cheaper than paying per ride. r > 54/2.40 = 22.5, so at 23 rides the pass becomes cheaper.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: break-even analysis with unit cost.
Q108. A 2.5-pound bag of rice costs $4.75. What is the cost per pound (to the nearest cent)?
Correct Answer: C
Explanation: Unit price = 4.75 ÷ 2.5 = 1.90 per pound.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate.
Explanation: Unit price = 4.75 ÷ 2.5 = 1.90 per pound.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate.
Q109. A contractor needs 520 feet of cable. Cable is sold in 50-foot rolls. Each roll has 2 feet that cannot be used due to damaged ends. What is the minimum number of rolls needed?
Correct Answer: B
Explanation: Usable per roll = 50 − 2 = 48 feet. Rolls needed = 520/48 ≈ 10.83, so you must buy 11 rolls.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: effective yield per unit and rounding up.
Explanation: Usable per roll = 50 − 2 = 48 feet. Rolls needed = 520/48 ≈ 10.83, so you must buy 11 rolls.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: effective yield per unit and rounding up.
Q110. A runner’s pace is 7 minutes 30 seconds per mile. About how long will it take to run 6.4 miles?
Correct Answer: C
Explanation: 7 minutes 30 seconds per mile is 7.5 minutes per mile. Time = 6.4 × 7.5 = 48.0 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate with time conversion.
Explanation: 7 minutes 30 seconds per mile is 7.5 minutes per mile. Time = 6.4 × 7.5 = 48.0 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate with time conversion.
Q111. A rectangle has a perimeter of 54 inches. If the length is 3 inches more than the width, what is the width?
Correct Answer: B
Explanation: Let width be w and length be w + 3. Perimeter: 2(w + w + 3) = 54 → 4w + 6 = 54 → 4w = 48 → w = 12.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: perimeter and algebraic setup.
Explanation: Let width be w and length be w + 3. Perimeter: 2(w + w + 3) = 54 → 4w + 6 = 54 → 4w = 48 → w = 12.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: perimeter and algebraic setup.
Q112. A 2.8% solution contains 420 grams total. How many grams of the active ingredient are in the solution (to the nearest tenth)?
Correct Answer: C
Explanation: Active ingredient = 0.028 × 420 = 11.76 grams, which rounds to 11.8 g.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a quantity.
Explanation: Active ingredient = 0.028 × 420 = 11.76 grams, which rounds to 11.8 g.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a quantity.
Q113. A printer cartridge can print 1,250 pages. If a print job uses 18 pages per document and you must print 64 documents, how many pages will be printed and how many pages of cartridge capacity will remain?
Correct Answer: A
Explanation: Pages printed = 64 × 18 = 1,152. Remaining capacity = 1,250 − 1,152 = 98 pages.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: multiplication and subtraction with a capacity limit.
Explanation: Pages printed = 64 × 18 = 1,152. Remaining capacity = 1,250 − 1,152 = 98 pages.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: multiplication and subtraction with a capacity limit.
Q114. A car rental charges $38 per day plus $0.22 per mile. If the bill for 3 days and 410 miles is $214.20, what should the correct bill be?
Correct Answer: A
Explanation: Daily charge = 3 × 38 = 114. Mileage charge = 410 × 0.22 = 90.20. Total = 114 + 90.20 = 204.20.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: linear cost calculation.
Explanation: Daily charge = 3 × 38 = 114. Mileage charge = 410 × 0.22 = 90.20. Total = 114 + 90.20 = 204.20.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: linear cost calculation.
Q115. A meal costs $18.40. A tip is 18% of the meal cost, and sales tax is 7% of the meal cost. What is the total amount paid (nearest cent), assuming both tip and tax are calculated on the meal cost only?
Correct Answer: C
Explanation: Tip = 18.40 × 0.18 = 3.312. Tax = 18.40 × 0.07 = 1.288. Total = 18.40 + 3.312 + 1.288 = 23.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent calculations and totals.
Explanation: Tip = 18.40 × 0.18 = 3.312. Tax = 18.40 × 0.07 = 1.288. Total = 18.40 + 3.312 + 1.288 = 23.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent calculations and totals.
Q116. A store has 240 items. On Monday it sells 15% of them, and on Tuesday it sells 25% of the remaining items. How many items are left after Tuesday?
Correct Answer: B
Explanation: After Monday: 15% of 240 is 36 sold, leaving 204. Tuesday sells 25% of 204, which is 51, leaving 204 − 51 = 153.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent changes on a changing base.
Explanation: After Monday: 15% of 240 is 36 sold, leaving 204. Tuesday sells 25% of 204, which is 51, leaving 204 − 51 = 153.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent changes on a changing base.
Q117. A runner completes 5/6 of a 24-mile route. How many miles remain?
Correct Answer: B
Explanation: Completed distance = (5/6) × 24 = 20 miles. Remaining = 24 − 20 = 4 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and subtraction.
Explanation: Completed distance = (5/6) × 24 = 20 miles. Remaining = 24 − 20 = 4 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and subtraction.
Q118. A machine produces 18 parts every 12 minutes at a steady rate. About how many parts can it produce in 7.5 hours?
Correct Answer: C
Explanation: Rate = 18/12 = 1.5 parts per minute. 7.5 hours = 450 minutes. Parts = 1.5 × 450 = 675.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate with time conversion.
Explanation: Rate = 18/12 = 1.5 parts per minute. 7.5 hours = 450 minutes. Parts = 1.5 × 450 = 675.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate with time conversion.
Q119. A $9,600 savings account is split into two accounts. One earns 3% annual simple interest and the other earns 5%. If the total annual interest is $408, how much is invested at 5%?
Correct Answer: C
Explanation: Let x be at 5%, so 9,600 − x is at 3%. Total interest: 0.05x + 0.03(9,600 − x) = 408 → 0.02x + 288 = 408 → 0.02x = 120 → x = 6,000.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted interest and solving a linear equation.
Explanation: Let x be at 5%, so 9,600 − x is at 3%. Total interest: 0.05x + 0.03(9,600 − x) = 408 → 0.02x + 288 = 408 → 0.02x = 120 → x = 6,000.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted interest and solving a linear equation.
Q120. A worker’s efficiency improves so that a task takes 20% less time. If the task originally took 2 hours 15 minutes, how long does it take now?
Correct Answer: C
Explanation: 2 hours 15 minutes is 135 minutes. 20% less time means 80% of original: 0.8 × 135 = 108 minutes = 1 hour 48 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent decrease applied to time.
Explanation: 2 hours 15 minutes is 135 minutes. 20% less time means 80% of original: 0.8 × 135 = 108 minutes = 1 hour 48 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent decrease applied to time.
Q121. A shipment has 3 types of boxes: small, medium, and large in a ratio of 2:3:5. If there are 160 boxes total, how many medium boxes are there?
Correct Answer: B
Explanation: Total parts = 2 + 3 + 5 = 10. Each part = 160/10 = 16. Medium boxes = 3 parts = 3 × 16 = 48.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: multi-part ratios to totals.
Explanation: Total parts = 2 + 3 + 5 = 10. Each part = 160/10 = 16. Medium boxes = 3 parts = 3 × 16 = 48.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: multi-part ratios to totals.
Q122. A company’s monthly electricity bill is $1,250. If usage drops by 12% and the rate per kWh rises by 5%, what is the new bill (nearest cent), assuming the bill is proportional to usage × rate?
Correct Answer: A
Explanation: New bill factor = 0.88 × 1.05 = 0.924. New bill = 1,250 × 0.924 = 1,155.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compound percent change by multiplication.
Explanation: New bill factor = 0.88 × 1.05 = 0.924. New bill = 1,250 × 0.924 = 1,155.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compound percent change by multiplication.
Q123. A rectangular room is 18 ft by 14 ft. Carpet is sold in rolls that cover 30 square feet each. If 8% extra is required for waste, how many rolls are needed?
Correct Answer: B
Explanation: Room area = 18 × 14 = 252 sq ft. Add 8% waste: 252 × 1.08 = 272.16 sq ft. Rolls needed = 272.16/30 ≈ 9.07, so round up to 10 rolls.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area, percent increase, and rounding up.
Explanation: Room area = 18 × 14 = 252 sq ft. Add 8% waste: 252 × 1.08 = 272.16 sq ft. Rolls needed = 272.16/30 ≈ 9.07, so round up to 10 rolls.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area, percent increase, and rounding up.
Q124. A discount store sells socks in packs of 6 for $7.50. A competitor sells packs of 8 for $9.84. Which is cheaper per sock and by how much (nearest cent)?
Correct Answer: D
Explanation: 6-pack unit price = 7.50/6 = $1.25 per sock. 8-pack unit price = 9.84/8 = $1.23 per sock. The 8-pack is cheaper by $1.25 − $1.23 = $0.02 per sock.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate comparison.
Explanation: 6-pack unit price = 7.50/6 = $1.25 per sock. 8-pack unit price = 9.84/8 = $1.23 per sock. The 8-pack is cheaper by $1.25 − $1.23 = $0.02 per sock.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate comparison.
Q125. A company plans to produce 3,600 units over 15 days at a constant daily rate. After 6 days, it has produced 1,440 units. How many units per day must it produce for the remaining days to meet the goal?
Correct Answer: D
Explanation: Remaining units = 3,600 − 1,440 = 2,160. Remaining days = 15 − 6 = 9. Required rate = 2,160/9 = 240 units per day.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: remaining work and required rate.
Explanation: Remaining units = 3,600 − 1,440 = 2,160. Remaining days = 15 − 6 = 9. Required rate = 2,160/9 = 240 units per day.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: remaining work and required rate.
Q126. A water pipe leaks at 0.66 liters per minute. If the leak continues for 3 hours 20 minutes, how many liters are lost?
Correct Answer: C
Explanation: Time = 3 hours 20 minutes = 200 minutes. Loss = 0.66 × 200 = 132 liters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate × time with time conversion.
Explanation: Time = 3 hours 20 minutes = 200 minutes. Loss = 0.66 × 200 = 132 liters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate × time with time conversion.
Q127. A store mixes two coffees: one costs $9 per pound and the other costs $15 per pound. How many pounds of the $15 coffee are needed to make 20 pounds of a blend that costs $12 per pound?
Correct Answer: C
Explanation: Let x be pounds of $15 coffee, so 20 − x is $9 coffee. Total cost: 15x + 9(20 − x) = 12 × 20 = 240. Solve: 15x + 180 − 9x = 240 → 6x = 60 → x = 10.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average/mixture cost.
Explanation: Let x be pounds of $15 coffee, so 20 − x is $9 coffee. Total cost: 15x + 9(20 − x) = 12 × 20 = 240. Solve: 15x + 180 − 9x = 240 → 6x = 60 → x = 10.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average/mixture cost.
Q128. A phone battery is at 88%. After 3 hours it is at 70%. Assuming a constant drain rate, how many percentage points per hour is the battery draining?
Correct Answer: B
Explanation: Battery drops 88 − 70 = 18 percentage points in 3 hours. Drain rate = 18/3 = 6 points per hour.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate of change (difference ÷ time).
Explanation: Battery drops 88 − 70 = 18 percentage points in 3 hours. Drain rate = 18/3 = 6 points per hour.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate of change (difference ÷ time).
Q129. A worker is scheduled for 7.5 hours. The worker takes two 12-minute breaks and one 30-minute lunch. How many minutes of actual working time are scheduled?
Correct Answer: A
Explanation: Total scheduled time = 7.5 hours = 450 minutes. Breaks and lunch total = 12 + 12 + 30 = 54 minutes. Working time = 450 − 54 = 396 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: time conversion and subtraction.
Explanation: Total scheduled time = 7.5 hours = 450 minutes. Breaks and lunch total = 12 + 12 + 30 = 54 minutes. Working time = 450 − 54 = 396 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: time conversion and subtraction.
Q130. A company has 480 employees. If 3/8 work remotely, how many employees do NOT work remotely?
Correct Answer: C
Explanation: Remote employees = (3/8) × 480 = 180. Non-remote = 480 − 180 = 300.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and complement.
Explanation: Remote employees = (3/8) × 480 = 180. Non-remote = 480 − 180 = 300.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and complement.
Q131. A shipment is supposed to be 2,735 pounds. It arrives at 2,612.5 pounds. What percent of the expected weight arrived (nearest tenth)?
Correct Answer: C
Explanation: Percent received = 2,612.5 ÷ 2,735 ≈ 0.9552. Convert to percent: 0.9552 × 100 ≈ 95.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of expected value.
Explanation: Percent received = 2,612.5 ÷ 2,735 ≈ 0.9552. Convert to percent: 0.9552 × 100 ≈ 95.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of expected value.
Q132. A 40-question quiz is worth 100 points total. Each correct answer is worth 2.5 points. If a student scores 82.5 points, how many questions were answered correctly?
Correct Answer: D
Explanation: Correct answers = 82.5 ÷ 2.5 = 33.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion from points to items.
Explanation: Correct answers = 82.5 ÷ 2.5 = 33.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion from points to items.
Q133. A store sells a tool for $84. If the store wants a 25% profit based on cost, what was the cost of the tool?
Correct Answer: C
Explanation: A 25% profit on cost means selling price = cost × 1.25. So cost = 84 ÷ 1.25 = 67.20.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: markup/profit based on cost.
Explanation: A 25% profit on cost means selling price = cost × 1.25. So cost = 84 ÷ 1.25 = 67.20.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: markup/profit based on cost.
Q134. A project requires 18.75 hours of labor. If workers are paid in 15-minute increments, how many 15-minute increments will be billed?
Correct Answer: C
Explanation: There are 4 fifteen-minute increments per hour. Increments billed = 18.75 × 4 = 75 increments.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: time conversion to fixed increments.
Explanation: There are 4 fifteen-minute increments per hour. Increments billed = 18.75 × 4 = 75 increments.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: time conversion to fixed increments.
Q135. A $360 payment is split so that 5/12 goes to savings and the rest goes to expenses. How much goes to expenses?
Correct Answer: C
Explanation: Savings = (5/12) × 360 = 150. Expenses = 360 − 150 = 210.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and remainder.
Explanation: Savings = (5/12) × 360 = 150. Expenses = 360 − 150 = 210.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and remainder.
Q136. A car travels 84 miles using 3.5 gallons. At the same rate, how many gallons are needed to travel 240 miles (nearest tenth)?
Correct Answer: C
Explanation: Gallons per mile = 3.5/84. Gallons for 240 miles = 240 × (3.5/84) = 10.0 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional scaling with unit rate.
Explanation: Gallons per mile = 3.5/84. Gallons for 240 miles = 240 × (3.5/84) = 10.0 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional scaling with unit rate.
Q137. A box contains 30 bolts. If 20% are removed, and then 2 bolts are added, how many bolts are in the box now?
Correct Answer: B
Explanation: Removing 20% leaves 80% of 30, which is 24. Then add 2 bolts: 24 + 2 = 26.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change and addition.
Explanation: Removing 20% leaves 80% of 30, which is 24. Then add 2 bolts: 24 + 2 = 26.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change and addition.
Q138. A store sells a bundle of 4 items for $58. If the bundle price is 12% less than buying the items individually, what is the individual total price before the discount (nearest cent)?
Correct Answer: B
Explanation: Bundle price is 88% of individual total: 0.88 × total = 58. Total = 58/0.88 = 65.909…, which rounds to $65.91.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent using division.
Explanation: Bundle price is 88% of individual total: 0.88 × total = 58. Total = 58/0.88 = 65.909…, which rounds to $65.91.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent using division.
Q139. A project has 3 phases lasting 2.5 hours, 3.75 hours, and 1.6 hours. What is the total time in hours (nearest hundredth)?
Correct Answer: B
Explanation: Total time = 2.5 + 3.75 + 1.6 = 7.85 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: adding decimals.
Explanation: Total time = 2.5 + 3.75 + 1.6 = 7.85 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: adding decimals.
Q140. A ladder is 20 ft long and reaches 16 ft up a wall. How far is the base from the wall?
Correct Answer: C
Explanation: Base distance = √(20² − 16²) = √(400 − 256) = √144 = 12 ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: right-triangle relationship (Pythagorean theorem).
Explanation: Base distance = √(20² − 16²) = √(400 − 256) = √144 = 12 ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: right-triangle relationship (Pythagorean theorem).
Q141. A worker completes 42% of a task in 2.7 hours at a constant rate. About how many hours will the full task take (nearest tenth)?
Correct Answer: C
Explanation: If 42% takes 2.7 hours, then 100% takes 2.7 ÷ 0.42 ≈ 6.4286 hours, which rounds to 6.4 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional reasoning with rates.
Explanation: If 42% takes 2.7 hours, then 100% takes 2.7 ÷ 0.42 ≈ 6.4286 hours, which rounds to 6.4 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional reasoning with rates.
Q142. A store buys a batch of 320 items. If 7.5% are damaged in transit, how many undamaged items remain?
Correct Answer: B
Explanation: Damaged items = 0.075 × 320 = 24. Undamaged = 320 − 24 = 296.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent loss and subtraction.
Explanation: Damaged items = 0.075 × 320 = 24. Undamaged = 320 − 24 = 296.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent loss and subtraction.
Q143. A container holds 18 quarts. It is currently 10 quarts full. What percent of the container is full (nearest tenth)?
Correct Answer: B
Explanation: Percent full = 10/18 ≈ 0.5556. Convert to percent: 0.5556 × 100 ≈ 55.6%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction to percent conversion.
Explanation: Percent full = 10/18 ≈ 0.5556. Convert to percent: 0.5556 × 100 ≈ 55.6%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction to percent conversion.
Q144. A worker uses 3/10 of a 2.5-gallon container of cleaner. How many ounces of cleaner were used? (1 gallon = 128 ounces)
Correct Answer: C
Explanation: Used gallons = (3/10) × 2.5 = 0.75 gallons. Convert to ounces: 0.75 × 128 = 96 ounces.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fractions and unit conversion.
Explanation: Used gallons = (3/10) × 2.5 = 0.75 gallons. Convert to ounces: 0.75 × 128 = 96 ounces.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fractions and unit conversion.
Q145. A store offers 30% off, then applies an additional 5% off the discounted price. If the original price is $240, what is the final price?
Correct Answer: B
Explanation: After 30% off: 240 × 0.70 = 168. After another 5% off: 168 × 0.95 = 159.60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive discounts are multiplicative.
Explanation: After 30% off: 240 × 0.70 = 168. After another 5% off: 168 × 0.95 = 159.60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive discounts are multiplicative.
Q146. A vehicle travels 180 miles using 6 gallons of fuel. If fuel costs $3.85 per gallon, what is the fuel cost per mile (nearest cent)?
Correct Answer: C
Explanation: Cost per mile = (6 × 3.85)/180 = 23.10/180 = 0.1283…, which rounds to $0.13 per mile.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit cost per mile.
Explanation: Cost per mile = (6 × 3.85)/180 = 23.10/180 = 0.1283…, which rounds to $0.13 per mile.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit cost per mile.
Q147. A worker has $2,250 of expenses. If rent is 44% of expenses and utilities are 12% of expenses, how much is spent on rent plus utilities?
Correct Answer: C
Explanation: Rent + utilities = (44% + 12%) = 56% of 2,250. Amount = 0.56 × 2,250 = 1,260.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combining percents of a total.
Explanation: Rent + utilities = (44% + 12%) = 56% of 2,250. Amount = 0.56 × 2,250 = 1,260.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combining percents of a total.
Q148. A factory needs to ship 2,450 pounds of material. Each pallet can hold 175 pounds. How many pallets are needed?
Correct Answer: B
Explanation: Pallets needed = 2,450 ÷ 175 = 14 exactly (since 175 × 14 = 2,450).
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: dividing a total by capacity.
Explanation: Pallets needed = 2,450 ÷ 175 = 14 exactly (since 175 × 14 = 2,450).
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: dividing a total by capacity.
Q149. A store sells pens for $1.35 each or 10 for $12. If you need 28 pens, what is the least cost?
Correct Answer: C
Explanation: Buy two 10-packs for $24 (20 pens). Remaining 8 pens at $1.35 each cost $10.80. Total = 24 + 10.80 = $34.80, which is less than buying all individually (28 × 1.35 = $37.80).
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: minimizing cost using bundle pricing.
Explanation: Buy two 10-packs for $24 (20 pens). Remaining 8 pens at $1.35 each cost $10.80. Total = 24 + 10.80 = $34.80, which is less than buying all individually (28 × 1.35 = $37.80).
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: minimizing cost using bundle pricing.
Q150. A worker’s hourly wage is increased from $22.50 to $24.30. What is the percent increase (nearest tenth)?
Correct Answer: B
Explanation: Increase = 24.30 − 22.50 = 1.80. Percent increase = 1.80/22.50 = 0.08. Convert to percent: 8.0%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change.
Explanation: Increase = 24.30 − 22.50 = 1.80. Percent increase = 1.80/22.50 = 0.08. Convert to percent: 8.0%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change.
Q151. A contractor estimates a job will cost $2,400 in materials. The supplier gives an 8% discount on materials, then the contractor pays a $85 delivery fee. What is the final cost?
Correct Answer: B
Explanation: Apply the 8% discount: 2,400 × 0.92 = 2,208. Then add the $85 delivery fee: 2,208 + 85 = 2,293.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount plus fixed fee.
Explanation: Apply the 8% discount: 2,400 × 0.92 = 2,208. Then add the $85 delivery fee: 2,208 + 85 = 2,293.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount plus fixed fee.
Q152. A cyclist rides 18 miles at 12 mph, then 22 miles at 22 mph, and takes a 15-minute break in between. What is the average speed for the entire trip including the break (nearest tenth)?
Correct Answer: A
Explanation: Time = 18/12 = 1.5 hr, plus 22/22 = 1.0 hr, plus 0.25 hr break = 2.75 hr total. Average speed = 40 ÷ 2.75 ≈ 14.5 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed = total distance ÷ total time.
Explanation: Time = 18/12 = 1.5 hr, plus 22/22 = 1.0 hr, plus 0.25 hr break = 2.75 hr total. Average speed = 40 ÷ 2.75 ≈ 14.5 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed = total distance ÷ total time.
Q153. A shipment of bolts is divided into small, medium, and large boxes in a 5:7:8 ratio. If there are 400 boxes total, how many medium boxes are there?
Correct Answer: B
Explanation: Total parts = 5 + 7 + 8 = 20. Each part = 400/20 = 20. Medium boxes = 7 parts = 7 × 20 = 140.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios and proportional parts.
Explanation: Total parts = 5 + 7 + 8 = 20. Each part = 400/20 = 20. Medium boxes = 7 parts = 7 × 20 = 140.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratios and proportional parts.
Q154. After an 18% discount, a jacket costs $369. What was the original price (nearest cent)?
Correct Answer: A
Explanation: Discounted price is 82% of original: 0.82 × original = 369, so original = 369 ÷ 0.82 = $450.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent change using division.
Explanation: Discounted price is 82% of original: 0.82 × original = 369, so original = 369 ÷ 0.82 = $450.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent change using division.
Q155. A 12-liter solution is 30% alcohol. How many liters of water must be added to make the solution 18% alcohol?
Correct Answer: C
Explanation: Alcohol amount stays 0.30 × 12 = 3.6 L. After adding x liters of water, 3.6/(12 + x) = 0.18 → 12 + x = 20 → x = 8 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture/concentration with conserved component.
Explanation: Alcohol amount stays 0.30 × 12 = 3.6 L. After adding x liters of water, 3.6/(12 + x) = 0.18 → 12 + x = 20 → x = 8 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture/concentration with conserved component.
Q156. A batch has a 10% defect rate. If 3 items are selected independently, what is the probability that at least one is defective (nearest thousandth)?
Correct Answer: A
Explanation: Use the complement: probability none are defective is 0.9³ = 0.729. So probability at least one defective = 1 − 0.9³ = 0.271.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: complement probability with independent events.
Explanation: Use the complement: probability none are defective is 0.9³ = 0.729. So probability at least one defective = 1 − 0.9³ = 0.271.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: complement probability with independent events.
Q157. A worker earns $21 per hour for the first 40 hours and time-and-a-half for overtime. If the worker earned $1,029 in a week, how many hours were worked?
Correct Answer: C
Explanation: Regular pay = 40 × 21 = 840. Remaining pay = 1,029 − 840 = 189. Overtime rate = 1.5 × 21 = 31.50. Overtime hours = 189 ÷ 31.5 = 6. Total hours = 40 + 6 = 46.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise wage rates and solving for hours.
Explanation: Regular pay = 40 × 21 = 840. Remaining pay = 1,029 − 840 = 189. Overtime rate = 1.5 × 21 = 31.50. Overtime hours = 189 ÷ 31.5 = 6. Total hours = 40 + 6 = 46.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise wage rates and solving for hours.
Q158. One gallon of paint covers 350 square feet. A wall area totals 352 square feet, and 10% extra paint is needed for waste. How many whole gallons must be purchased?
Correct Answer: B
Explanation: Area with waste = 352 × 1.10 = 387.2 sq ft. One gallon covers 350 sq ft, so gallons needed = 387.2/350 ≈ 1.11. You must buy 2 whole gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: coverage rates, percent increase, and rounding up.
Explanation: Area with waste = 352 × 1.10 = 387.2 sq ft. One gallon covers 350 sq ft, so gallons needed = 387.2/350 ≈ 1.11. You must buy 2 whole gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: coverage rates, percent increase, and rounding up.
Q159. A course grade is 35% labs, 40% midterm, and 25% final exam. A student scores 92 on labs, 78 on the midterm, and 84 on the final. What is the overall average?
Correct Answer: A
Explanation: Weighted average = 0.35(92) + 0.40(78) + 0.25(84) = 84.4.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average.
Explanation: Weighted average = 0.35(92) + 0.40(78) + 0.25(84) = 84.4.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average.
Q160. Worker A can complete a job in 8 hours and Worker B can complete it in 12 hours. About how long will they take working together (nearest tenth)?
Correct Answer: A
Explanation: Combined rate = 1/8 + 1/12 = 3/24 + 2/24 = 5/24 job/hr. Time = 1 ÷ (5/24) = 24/5 = 4.8 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined work rates.
Explanation: Combined rate = 1/8 + 1/12 = 3/24 + 2/24 = 5/24 job/hr. Time = 1 ÷ (5/24) = 24/5 = 4.8 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined work rates.
Q161. A route is 3.6 kilometers long. Using 1 mile = 1.6 kilometers, how many miles is the route?
Correct Answer: C
Explanation: Miles = 3.6 ÷ 1.6 = 2.25 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion.
Explanation: Miles = 3.6 ÷ 1.6 = 2.25 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion.
Q162. A store marks up an item by 40% above cost, then offers 15% off the marked price. If the cost is $95, what is the sale price (nearest cent)?
Correct Answer: A
Explanation: Marked price = 95 × 1.40 = 133.00. Sale price = 133.00 × 0.85 = $113.05.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change.
Explanation: Marked price = 95 × 1.40 = 133.00. Sale price = 133.00 × 0.85 = $113.05.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change.
Q163. Adult tickets cost $16 and child tickets cost $10. If 188 tickets are sold for a total of $2,600, how many adult tickets were sold?
Correct Answer: B
Explanation: Let a be adult and c be child. a + c = 188 and 16a + 10c = 2,600. Substitute c = 188 − a: 16a + 10(188 − a) = 2,600 → 6a = 720 → a = 120.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: system of equations from totals.
Explanation: Let a be adult and c be child. a + c = 188 and 16a + 10c = 2,600. Substitute c = 188 − a: 16a + 10(188 − a) = 2,600 → 6a = 720 → a = 120.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: system of equations from totals.
Q164. A circular garden has an outer radius of 10 ft and an inner circular fountain with radius 6 ft. What is the area of the garden region (nearest tenth)?
Correct Answer: A
Explanation: Area of garden region = π(10² − 6²) = π(100 − 36) = 64π ≈ 201.1 sq ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area of circles and subtraction.
Explanation: Area of garden region = π(10² − 6²) = π(100 − 36) = 64π ≈ 201.1 sq ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area of circles and subtraction.
Q165. The average of 9 numbers is 14. After a tenth number is added, the average becomes 15.2. What is the tenth number?
Correct Answer: C
Explanation: Sum of 9 numbers = 9 × 14 = 126. Sum of 10 numbers = 10 × 15.2 = 152. Tenth number = 152 − 126 = 26.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Explanation: Sum of 9 numbers = 9 × 14 = 126. Sum of 10 numbers = 10 × 15.2 = 152. Tenth number = 152 − 126 = 26.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Q166. Shipping costs a $6 base fee plus $1.10 per pound for the first 12 pounds and $0.70 per pound for each pound over 12. What is the shipping cost for a 20-pound package?
Correct Answer: A
Explanation: Cost = 6 + 1.10(12) + 0.70(8) = 6 + 13.20 + 5.60 = 24.80.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise linear cost.
Explanation: Cost = 6 + 1.10(12) + 0.70(8) = 6 + 13.20 + 5.60 = 24.80.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: piecewise linear cost.
Q167. Which fraction is equal to 0.28 in simplest form?
Correct Answer: A
Explanation: 0.28 = 28/100. Divide numerator and denominator by 4: 28/100 = 7/25, which is simplest.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting decimals to simplified fractions.
Explanation: 0.28 = 28/100. Divide numerator and denominator by 4: 28/100 = 7/25, which is simplest.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting decimals to simplified fractions.
Q168. An account earns 5.5% annual simple interest. How much interest is earned on $4,500 over 18 months (nearest cent)?
Correct Answer: B
Explanation: Time = 18/12 = 1.5 years. Simple interest I = Prt = 4,500 × 0.055 × 1.5 = $371.25.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (I = Prt).
Explanation: Time = 18/12 = 1.5 years. Simple interest I = Prt = 4,500 × 0.055 × 1.5 = $371.25.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (I = Prt).
Q169. A package weighs 92 ounces. How many pounds is this weight? (16 ounces = 1 pound)
Correct Answer: C
Explanation: Pounds = 92 ÷ 16 = 5.75 lb.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion.
Explanation: Pounds = 92 ÷ 16 = 5.75 lb.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion.
Q170. A population increases by 6% one year and then decreases by 4% the next year. What is the overall percent change over the two years (nearest tenth)?
Correct Answer: A
Explanation: Successive changes multiply: 1.06 × 0.96 = 1.0176. Overall change = (1.0176 − 1) × 100 ≈ 1.8%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compound percent change.
Explanation: Successive changes multiply: 1.06 × 0.96 = 1.0176. Overall change = (1.0176 − 1) × 100 ≈ 1.8%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: compound percent change.
Q171. Three consecutive even integers have a sum of 156. What is the largest integer?
Correct Answer: C
Explanation: Let the integers be x, x+2, x+4. Then 3x + 6 = 156 → 3x = 150 → x = 50. Largest = x + 4 = 54.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: consecutive integers and algebra.
Explanation: Let the integers be x, x+2, x+4. Then 3x + 6 = 156 → 3x = 150 → x = 50. Largest = x + 4 = 54.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: consecutive integers and algebra.
Q172. A gym charges $11 per class, or you can buy a $45 membership that reduces the class cost to $6 per class. What is the minimum number of classes needed for the membership option to be cheaper?
Correct Answer: C
Explanation: Membership cost is 45 + 6n. Regular cost is 11n. Solve 45 + 6n < 11n → 45 < 5n → n > 9. So the minimum whole number is 10 classes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: break-even inequalities.
Explanation: Membership cost is 45 + 6n. Regular cost is 11n. Solve 45 + 6n < 11n → 45 < 5n → n > 9. So the minimum whole number is 10 classes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: break-even inequalities.
Q173. A rectangular box is 10 in long, 6 in wide, and 4 in high. Paint covers 94 square inches per ounce. How many ounces are needed to paint the top and all four sides (not the bottom)?
Correct Answer: B
Explanation: Area to paint = top (10×6)=60 plus sides 2(10×4)=80 and 2(6×4)=48. Total = 60+80+48 = 188 sq in. Ounces = 188/94 = 2.0 oz.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: surface area and coverage rate.
Explanation: Area to paint = top (10×6)=60 plus sides 2(10×4)=80 and 2(6×4)=48. Total = 60+80+48 = 188 sq in. Ounces = 188/94 = 2.0 oz.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: surface area and coverage rate.
Q174. A tank holds 32 gallons and currently contains 14 gallons. What percent of the tank is full (nearest tenth)?
Correct Answer: B
Explanation: Percent full = 14/32 = 0.4375. Convert to percent: 0.4375 × 100 = 43.8%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction to percent conversion.
Explanation: Percent full = 14/32 = 0.4375. Convert to percent: 0.4375 × 100 = 43.8%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction to percent conversion.
Q175. A car travels at 55 mph for 2 hours 18 minutes. How many miles does it travel?
Correct Answer: C
Explanation: Convert time: 2 hours 18 minutes = 2 + 18/60 = 2.3 hours. Distance = 55 × 2.3 = 126.5 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: distance = rate × time.
Explanation: Convert time: 2 hours 18 minutes = 2 + 18/60 = 2.3 hours. Distance = 55 × 2.3 = 126.5 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: distance = rate × time.
Q176. A 30-pound blend of nuts must cost $11.40 per pound. Nuts A cost $9.60 per pound and Nuts B cost $13.20 per pound. How many pounds of Nuts B are needed?
Correct Answer: C
Explanation: Let x be pounds of Nuts B. Then 30 − x pounds are Nuts A. Total cost: 13.2x + 9.6(30 − x) = 11.4(30) = 342. Solve: 13.2x + 288 − 9.6x = 342 → 3.6x = 54 → x = 15.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture cost using weighted averages.
Explanation: Let x be pounds of Nuts B. Then 30 − x pounds are Nuts A. Total cost: 13.2x + 9.6(30 − x) = 11.4(30) = 342. Solve: 13.2x + 288 − 9.6x = 342 → 3.6x = 54 → x = 15.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture cost using weighted averages.
Q177. A trip starts at 7:45 AM. Travel time is 1 hour 55 minutes, then a 35-minute stop, then 2 hours 10 minutes more. What is the arrival time?
Correct Answer: C
Explanation: Total elapsed time = 1:55 + 0:35 + 2:10 = 4:40. Add 4 hours 40 minutes to 7:45 AM to get 12:25 PM.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: adding elapsed times.
Explanation: Total elapsed time = 1:55 + 0:35 + 2:10 = 4:40. Add 4 hours 40 minutes to 7:45 AM to get 12:25 PM.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: adding elapsed times.
Q178. An hourly wage increases from $18.75 to $20.10. What is the percent increase (nearest tenth)?
Correct Answer: B
Explanation: Increase = 20.10 − 18.75 = 1.35. Percent increase = 1.35/18.75 = 0.072. Convert to percent: 7.2%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change.
Explanation: Increase = 20.10 − 18.75 = 1.35. Percent increase = 1.35/18.75 = 0.072. Convert to percent: 7.2%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change.
Q179. A store has 520 units in stock. It sells 18% on Saturday and then sells 10% of the remaining stock on Sunday. How many units remain after Sunday?
Correct Answer: A
Explanation: After Saturday: 520 × 0.82 = 426.4 units remain. After Sunday: 426.4 × 0.90 = 383.76, which is 384 units when counted as whole units.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent decreases on a changing base.
Explanation: After Saturday: 520 × 0.82 = 426.4 units remain. After Sunday: 426.4 × 0.90 = 383.76, which is 384 units when counted as whole units.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent decreases on a changing base.
Q180. A right triangle has legs of 7 inches and 24 inches. What is the length of the hypotenuse?
Correct Answer: C
Explanation: Use the Pythagorean theorem: √(7² + 24²) = √(49 + 576) = √625 = 25.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: Pythagorean theorem.
Explanation: Use the Pythagorean theorem: √(7² + 24²) = √(49 + 576) = √625 = 25.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: Pythagorean theorem.
Q181. A vehicle travels 420 miles using 14 gallons of fuel. If fuel costs $3.60 per gallon, what is the fuel cost per mile?
Correct Answer: B
Explanation: Total fuel cost = 14 × 3.60 = 50.40. Cost per mile = 50.40 ÷ 420 = 0.12.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit cost per mile.
Explanation: Total fuel cost = 14 × 3.60 = 50.40. Cost per mile = 50.40 ÷ 420 = 0.12.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit cost per mile.
Q182. Two numbers have a sum of 87. The larger number is 2 times the smaller number plus 9. What is the larger number?
Correct Answer: C
Explanation: Let s be the smaller number and L be the larger. L = 2s + 9 and s + L = 87 → s + 2s + 9 = 87 → 3s = 78 → s = 26. Then L = 2(26) + 9 = 61.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: translating words into equations.
Explanation: Let s be the smaller number and L be the larger. L = 2s + 9 and s + L = 87 → s + 2s + 9 = 87 → 3s = 78 → s = 26. Then L = 2(26) + 9 = 61.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: translating words into equations.
Q183. A monthly budget is $3,200. Rent is $1,180, food is 14% of the budget, and transportation is 9% of the budget. How much money is left for everything else?
Correct Answer: A
Explanation: Food = 0.14 × 3,200 = 448. Transportation = 0.09 × 3,200 = 288. Remaining = 3,200 − 1,180 − 448 − 288 = 1,284.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent allocations and remainder.
Explanation: Food = 0.14 × 3,200 = 448. Transportation = 0.09 × 3,200 = 288. Remaining = 3,200 − 1,180 − 448 − 288 = 1,284.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent allocations and remainder.
Q184. What decimal is equal to 9/16?
Correct Answer: B
Explanation: Divide 9 by 16: 9 ÷ 16 = 0.5625.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction to decimal conversion.
Explanation: Divide 9 by 16: 9 ÷ 16 = 0.5625.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction to decimal conversion.
Q185. A person wants to average 5,000 steps per day over 7 days. After 4 days, they have taken 18,200 steps. How many steps per day are needed for the remaining 3 days to reach the goal?
Correct Answer: C
Explanation: Total needed = 7 × 5,000 = 35,000 steps. Remaining = 35,000 − 18,200 = 16,800 steps over 3 days. Required per day = 16,800/3 = 5,600.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages, totals, and required remaining rate.
Explanation: Total needed = 7 × 5,000 = 35,000 steps. Remaining = 35,000 − 18,200 = 16,800 steps over 3 days. Required per day = 16,800/3 = 5,600.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages, totals, and required remaining rate.
Q186. A loan of $12,000 charges 9% annual simple interest. How much interest accrues in 8 months?
Correct Answer: C
Explanation: Time = 8/12 = 2/3 year. Interest = 12,000 × 0.09 × (2/3) = 12,000 × 0.06 = 720.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (I = Prt).
Explanation: Time = 8/12 = 2/3 year. Interest = 12,000 × 0.09 × (2/3) = 12,000 × 0.06 = 720.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (I = Prt).
Q187. A bag has 3 red marbles and 2 green marbles. Two marbles are drawn with replacement. What is the probability both marbles are red?
Correct Answer: C
Explanation: With replacement, the probability of red each draw is 3/5. Probability both red = (3/5)² = 9/25 = 0.36.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability with replacement (independent events).
Explanation: With replacement, the probability of red each draw is 3/5. Probability both red = (3/5)² = 9/25 = 0.36.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability with replacement (independent events).
Q188. A bottle contains 2.75 liters of juice. How many milliliters is this? (1 liter = 1,000 milliliters)
Correct Answer: C
Explanation: Multiply by 1,000: 2.75 L × 1,000 = 2,750 mL.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: metric unit conversion.
Explanation: Multiply by 1,000: 2.75 L × 1,000 = 2,750 mL.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: metric unit conversion.
Q189. A meal has 680 calories. If 30% come from protein and 25% come from fat, how many calories come from carbohydrates?
Correct Answer: C
Explanation: Protein + fat = 30% + 25% = 55%, so carbs are 45%. Carbs calories = 0.45 × 680 = 306.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent remainder of a total.
Explanation: Protein + fat = 30% + 25% = 55%, so carbs are 45%. Carbs calories = 0.45 × 680 = 306.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent remainder of a total.
Q190. Three numbers are consecutive terms of an arithmetic sequence: x, x + 4, and x + 10. If their sum is 125, what is the largest number?
Correct Answer: C
Explanation: Sum: x + (x + 4) + (x + 10) = 125 → 3x + 14 = 125 → 3x = 111 → x = 37. Largest = x + 10 = 47.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: arithmetic sequences and solving linear equations.
Explanation: Sum: x + (x + 4) + (x + 10) = 125 → 3x + 14 = 125 → 3x = 111 → x = 37. Largest = x + 10 = 47.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: arithmetic sequences and solving linear equations.
Q191. A rectangular storage bin measures 2.4 m by 1.5 m by 0.8 m. What is its volume?
Correct Answer: C
Explanation: Volume = length × width × height = 2.4 × 1.5 × 0.8 = 2.88 cubic meters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: volume of a rectangular prism.
Explanation: Volume = length × width × height = 2.4 × 1.5 × 0.8 = 2.88 cubic meters.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: volume of a rectangular prism.
Q192. An item costs $86. A 12% discount is applied, then 8.25% sales tax is charged on the discounted price. What is the final price (nearest cent)?
Correct Answer: A
Explanation: Discounted price = 86 × 0.88 = 75.68. Tax = 75.68 × 0.0825 = 6.24. Total = 75.68 + 6.24 = $81.92.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change with tax.
Explanation: Discounted price = 86 × 0.88 = 75.68. Tax = 75.68 × 0.0825 = 6.24. Total = 75.68 + 6.24 = $81.92.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent change with tax.
Q193. A student reads 45 pages of a 72-page chapter. What percent of the chapter has been read?
Correct Answer: C
Explanation: Percent read = 45/72 = 0.625. Convert to percent: 0.625 × 100 = 62.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting a fraction to a percent.
Explanation: Percent read = 45/72 = 0.625. Convert to percent: 0.625 × 100 = 62.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting a fraction to a percent.
Q194. A warehouse has 200 boxes. It ships out 25 boxes, then receives a 20% restock on the remaining boxes. How many boxes are in the warehouse after the restock?
Correct Answer: C
Explanation: After shipping: 200 − 25 = 175 boxes. A 20% restock adds 0.20 × 175 = 35 boxes. New total = 175 + 35 = 210.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase on a new base.
Explanation: After shipping: 200 − 25 = 175 boxes. A 20% restock adds 0.20 × 175 = 35 boxes. New total = 175 + 35 = 210.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase on a new base.
Q195. On a blueprint, 1.5 inches represents 4 feet. A wall measures 6.75 inches on the blueprint. What is the actual length of the wall?
Correct Answer: B
Explanation: Scale factor = 4 ft per 1.5 in. Actual length = 6.75 × (4/1.5) = 6.75 × 2.666… = 18 ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: scale and proportional reasoning.
Explanation: Scale factor = 4 ft per 1.5 in. Actual length = 6.75 × (4/1.5) = 6.75 × 2.666… = 18 ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: scale and proportional reasoning.
Q196. What is the median of the numbers 8, 12, 15, 15, 19, 22, and 30?
Correct Answer: A
Explanation: There are 7 numbers in order, so the median is the 4th number. The 4th number is 15.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: median of an ordered data set.
Explanation: There are 7 numbers in order, so the median is the 4th number. The 4th number is 15.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: median of an ordered data set.
Q197. A 64 GB drive has 7.5% of its capacity reserved for system files. If each video file is 3.2 GB, what is the maximum number of full video files the drive can store?
Correct Answer: B
Explanation: Usable capacity = 64 × 0.925 = 59.2 GB. Number of 3.2 GB files = 59.2/3.2 = 18.5, so the maximum whole number of files is 18.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent reduction and integer capacity.
Explanation: Usable capacity = 64 × 0.925 = 59.2 GB. Number of 3.2 GB files = 59.2/3.2 = 18.5, so the maximum whole number of files is 18.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent reduction and integer capacity.
Q198. A 30 ft by 18 ft patio is surrounded by a 2-ft-wide border on the outside. What is the area of the border?
Correct Answer: C
Explanation: Outer dimensions add 4 ft to each side: 34 × 22 = 748 sq ft. Patio area = 30 × 18 = 540 sq ft. Border area = 748 − 540 = 208 sq ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area difference using expanded dimensions.
Explanation: Outer dimensions add 4 ft to each side: 34 × 22 = 748 sq ft. Patio area = 30 × 18 = 540 sq ft. Border area = 748 − 540 = 208 sq ft.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area difference using expanded dimensions.
Q199. A crew of 14 workers can finish a job in 6 days at a constant rate. How many days will it take 9 workers to finish the same job at the same rate?
Correct Answer: B
Explanation: Total work = 14 × 6 = 84 worker-days. With 9 workers, days = 84/9 = 9.333…, which is 9 1/3 days.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: inverse proportion (workers × days = constant work).
Explanation: Total work = 14 × 6 = 84 worker-days. With 9 workers, days = 84/9 = 9.333…, which is 9 1/3 days.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: inverse proportion (workers × days = constant work).
Q200. A currency exchange charges a flat $4 fee. After the fee, each unit of foreign currency costs $1.18. If you start with $150, how many units can you buy (nearest tenth)?
Correct Answer: A
Explanation: Money available after fee = 150 − 4 = 146. Units = 146 ÷ 1.18 ≈ 123.7 units.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: subtract fixed fee and divide by unit rate.
Explanation: Money available after fee = 150 − 4 = 146. Units = 146 ÷ 1.18 ≈ 123.7 units.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: subtract fixed fee and divide by unit rate.
Q201. A museum sells adult tickets for $18 and student tickets for $12. If 36 adult tickets and 24 student tickets are sold, what is the total revenue?
Correct Answer: B
Explanation: Adult revenue = 36 × 18 = 648. Student revenue = 24 × 12 = 288. Total = 648 + 288 = 936.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: total cost from unit prices.
Explanation: Adult revenue = 36 × 18 = 648. Student revenue = 24 × 12 = 288. Total = 648 + 288 = 936.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: total cost from unit prices.
Q202. A purchase totals $54.16 after an 8% sales tax is added. What was the pre-tax price (nearest cent)?
Correct Answer: A
Explanation: Total = pre-tax × 1.08, so pre-tax = 54.16 ÷ 1.08 = $50.15.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent (remove sales tax).
Explanation: Total = pre-tax × 1.08, so pre-tax = 54.16 ÷ 1.08 = $50.15.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent (remove sales tax).
Q203. Detergent A is 18 oz for $5.94. Detergent B is 32 oz for $9.92. Which is cheaper per ounce and by how much (nearest cent)?
Correct Answer: D
Explanation: Unit price A = 5.94/18 = $0.33 per oz. Unit price B = 9.92/32 = $0.31 per oz. B is cheaper by about $0.02 per oz.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate comparison.
Explanation: Unit price A = 5.94/18 = $0.33 per oz. Unit price B = 9.92/32 = $0.31 per oz. B is cheaper by about $0.02 per oz.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate comparison.
Q204. A warehouse has 84 yards of rope. If 7/12 of the rope is used, how many yards remain?
Correct Answer: B
Explanation: Used amount = (7/12) × 84 = 49. Remaining = 84 − 49 = 35.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and remainder.
Explanation: Used amount = (7/12) × 84 = 49. Remaining = 84 − 49 = 35.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and remainder.
Q205. Machine A completes one part every 15 minutes and Machine B completes one part every 24 minutes. Working together, about how many parts can they complete in 2 hours?
Correct Answer: C
Explanation: In 120 minutes, Machine A makes 120/15 = 8 parts and Machine B makes 120/24 = 5 parts. Together they make 8 + 5 = 13 parts.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined production rates.
Explanation: In 120 minutes, Machine A makes 120/15 = 8 parts and Machine B makes 120/24 = 5 parts. Together they make 8 + 5 = 13 parts.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined production rates.
Q206. A shop mixes 10 lb of coffee at $4.20/lb with 25 lb of coffee at $6.00/lb. What is the cost per pound of the mixture (nearest cent)?
Correct Answer: A
Explanation: Total cost = 10×4.20 + 25×6.00 = 42 + 150 = 192. Total pounds = 35. Cost per pound = 192/35 = $5.49.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average in mixture pricing.
Explanation: Total cost = 10×4.20 + 25×6.00 = 42 + 150 = 192. Total pounds = 35. Cost per pound = 192/35 = $5.49.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average in mixture pricing.
Q207. A factory produced 480 units last week and 522 units this week. What is the percent increase (nearest tenth)?
Correct Answer: C
Explanation: Increase = 522 − 480 = 42. Percent increase = 42/480 = 0.0875 = 8.8%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change.
Explanation: Increase = 522 − 480 = 42. Percent increase = 42/480 = 0.0875 = 8.8%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent change.
Q208. An account earns 4.2% annual simple interest. How much interest is earned on $7,800 over 9 months (nearest cent)?
Correct Answer: A
Explanation: Time = 9/12 = 0.75 years. Interest I = Prt = 7,800 × 0.042 × 0.75 = $245.70.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (I = Prt).
Explanation: Time = 9/12 = 0.75 years. Interest I = Prt = 7,800 × 0.042 × 0.75 = $245.70.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (I = Prt).
Q209. A box contains 6 blue markers and 4 yellow markers. Three markers are drawn without replacement. What is the probability all three are blue (nearest thousandth)?
Correct Answer: A
Explanation: P(all blue) = (6/10)×(5/9)×(4/8) = 0.167.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability without replacement.
Explanation: P(all blue) = (6/10)×(5/9)×(4/8) = 0.167.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: probability without replacement.
Q210. A triangular sign has a base of 18 inches and a height of 7.5 inches. What is its area?
Correct Answer: C
Explanation: Area of a triangle = (1/2) × base × height = 0.5 × 18 × 7.5 = 67.5 square inches.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area of a triangle.
Explanation: Area of a triangle = (1/2) × base × height = 0.5 × 18 × 7.5 = 67.5 square inches.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area of a triangle.
Q211. The average of 8 numbers is 19. If the number 31 is removed, what is the average of the remaining 7 numbers (nearest tenth)?
Correct Answer: A
Explanation: Sum of 8 numbers = 8 × 19 = 152. Remove 31 → remaining sum = 121. New average = 121/7 ≈ 17.3.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Explanation: Sum of 8 numbers = 8 × 19 = 152. Remove 31 → remaining sum = 121. New average = 121/7 ≈ 17.3.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Q212. Shipping Company A charges $9.50 plus $0.65 per pound. Company B charges $5.00 plus $0.85 per pound. For what package weight do both companies charge the same?
Correct Answer: C
Explanation: Set costs equal: 9.50 + 0.65w = 5.00 + 0.85w. Subtract 0.65w and 5.00: 4.50 = 0.20w → w = 22.5 lb.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: break-even point using linear equations.
Explanation: Set costs equal: 9.50 + 0.65w = 5.00 + 0.85w. Subtract 0.65w and 5.00: 4.50 = 0.20w → w = 22.5 lb.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: break-even point using linear equations.
Q213. A budget allocates 28% to housing and 37% to transportation. If the total budget is $2,850, how much is allocated to all other categories?
Correct Answer: A
Explanation: Other percent = 100% − 28% − 37% = 35%. Amount = 0.35 × 2,850 = 997.50.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent remainder of a total.
Explanation: Other percent = 100% − 28% − 37% = 35%. Amount = 0.35 × 2,850 = 997.50.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent remainder of a total.
Q214. Which fraction is equal to 0.375 in simplest form?
Correct Answer: A
Explanation: 0.375 = 375/1000. Divide by 125 to simplify: 375/1000 = 3/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting decimals to simplified fractions.
Explanation: 0.375 = 375/1000. Divide by 125 to simplify: 375/1000 = 3/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting decimals to simplified fractions.
Q215. A sequence follows a pattern: 6, 9, 13.5, 20.25, … What is the next number?
Correct Answer: C
Explanation: Each term is multiplied by 1.5: 6×1.5=9, 9×1.5=13.5, 13.5×1.5=20.25, so next = 20.25×1.5 = 30.375.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: recognizing multiplicative patterns.
Explanation: Each term is multiplied by 1.5: 6×1.5=9, 9×1.5=13.5, 13.5×1.5=20.25, so next = 20.25×1.5 = 30.375.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: recognizing multiplicative patterns.
Q216. A night shift runs from 9:20 PM to 4:50 AM. If the worker takes a 45-minute unpaid break, how many hours and minutes are paid working time?
Correct Answer: B
Explanation: Elapsed time from 9:20 PM to 4:50 AM is 7 hours 30 minutes. Subtract the 45-minute break: 7:30 − 0:45 = 6:45.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: elapsed time across midnight and subtraction.
Explanation: Elapsed time from 9:20 PM to 4:50 AM is 7 hours 30 minutes. Subtract the 45-minute break: 7:30 − 0:45 = 6:45.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: elapsed time across midnight and subtraction.
Q217. Using π ≈ 3.14, what is the volume of a cylinder with radius 3 cm and height 10 cm?
Correct Answer: C
Explanation: Volume = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cm³.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: volume of a cylinder.
Explanation: Volume = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cm³.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: volume of a cylinder.
Q218. A tool costs $125. Its price increases by 12% and then later decreases by 10%. What is the final price (nearest cent)?
Correct Answer: A
Explanation: After 12% increase: 125 × 1.12 = 140.00. After 10% decrease: 140.00 × 0.90 = $126.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent changes are multiplicative.
Explanation: After 12% increase: 125 × 1.12 = 140.00. After 10% decrease: 140.00 × 0.90 = $126.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent changes are multiplicative.
Q219. A delivery route is 250 miles. If 3/5 of the route is completed, how many miles remain?
Correct Answer: B
Explanation: Completed distance = (3/5) × 250 = 150 miles. Remaining = 250 − 150 = 100 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and remainder.
Explanation: Completed distance = (3/5) × 250 = 150 miles. Remaining = 250 − 150 = 100 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a whole and remainder.
Q220. An alloy is 60% copper and 25% zinc, with the rest tin. If you have 8 kg of the alloy, how many kilograms are tin?
Correct Answer: C
Explanation: Tin percent = 100% − 60% − 25% = 15%. Tin mass = 0.15 × 8 = 1.2 kg.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent composition and remainder.
Explanation: Tin percent = 100% − 60% − 25% = 15%. Tin mass = 0.15 × 8 = 1.2 kg.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent composition and remainder.
Q221. A warehouse must ship 1,370 lb of material. Each crate can hold 95 lb. What is the minimum number of crates needed?
Correct Answer: C
Explanation: Crates needed = 1,370 ÷ 95 ≈ 14.42, so you must round up to 15 crates.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: capacity division and rounding up.
Explanation: Crates needed = 1,370 ÷ 95 ≈ 14.42, so you must round up to 15 crates.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: capacity division and rounding up.
Q222. A train travels 150 kilometers in 2.5 hours. What is its average speed in kilometers per hour?
Correct Answer: B
Explanation: Average speed = distance ÷ time = 150 ÷ 2.5 = 60 km/h.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average rate (distance ÷ time).
Explanation: Average speed = distance ÷ time = 150 ÷ 2.5 = 60 km/h.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average rate (distance ÷ time).
Q223. An appliance is priced at $160. A 15% discount is applied, then a $20 coupon is used. What is the final price?
Correct Answer: A
Explanation: After 15% discount: 160 × 0.85 = 136. Then subtract the $20 coupon: 136 − 20 = 116.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount followed by fixed deduction.
Explanation: After 15% discount: 160 × 0.85 = 136. Then subtract the $20 coupon: 136 − 20 = 116.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount followed by fixed deduction.
Q224. A fair coin is flipped 3 times. What is the probability of getting at least one head?
Correct Answer: D
Explanation: Use the complement: probability of no heads (all tails) is (1/2)³ = 1/8. So probability of at least one head = 1 − 1/8 = 7/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: complement probability.
Explanation: Use the complement: probability of no heads (all tails) is (1/2)³ = 1/8. So probability of at least one head = 1 − 1/8 = 7/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: complement probability.
Q225. 40% of a number is 18. What is the number?
Correct Answer: C
Explanation: If 0.40 × n = 18, then n = 18 ÷ 0.40 = 45.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving for a whole from a percent.
Explanation: If 0.40 × n = 18, then n = 18 ÷ 0.40 = 45.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving for a whole from a percent.
Q226. A rectangle has perimeter 84 cm. Its length is 2.5 times its width. What is the width?
Correct Answer: B
Explanation: Let width = w and length = 2.5w. Perimeter: 2(w + 2.5w) = 84 → 7w = 84 → w = 12 cm.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: perimeter and algebra.
Explanation: Let width = w and length = 2.5w. Perimeter: 2(w + 2.5w) = 84 → 7w = 84 → w = 12 cm.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: perimeter and algebra.
Q227. The average of 5 numbers is 26. Four of the numbers are 18, 24, 29, and 31. What is the fifth number?
Correct Answer: C
Explanation: Sum of 5 numbers = 5 × 26 = 130. Sum of known four = 102. Fifth number = 130 − 102 = 28.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average and missing value.
Explanation: Sum of 5 numbers = 5 × 26 = 130. Sum of known four = 102. Fifth number = 130 − 102 = 28.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average and missing value.
Q228. A car averages 27 miles per gallon. About how many gallons are needed to drive 486 miles?
Correct Answer: C
Explanation: Gallons needed = 486 ÷ 27 = 18.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate (miles per gallon).
Explanation: Gallons needed = 486 ÷ 27 = 18.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate (miles per gallon).
Q229. What percent is equal to 11/20?
Correct Answer: C
Explanation: 11/20 = 0.55. Convert to percent: 0.55 × 100 = 55%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction to percent conversion.
Explanation: 11/20 = 0.55. Convert to percent: 0.55 × 100 = 55%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction to percent conversion.
Q230. A store makes a profit that is 20% of the selling price. If an item sells for $250, what was the cost to the store?
Correct Answer: C
Explanation: Profit = 20% of 250 = 50. Cost = 250 − 50 = 200.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of selling price and subtraction.
Explanation: Profit = 20% of 250 = 50. Cost = 250 − 50 = 200.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of selling price and subtraction.
Q231. A container holds 3.5 gallons of liquid. How many quarts is this? (1 gallon = 4 quarts)
Correct Answer: B
Explanation: Quarts = 3.5 × 4 = 14 quarts.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion.
Explanation: Quarts = 3.5 × 4 = 14 quarts.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion.
Q232. What is 30% of 80% of 500?
Correct Answer: C
Explanation: Compute 80% of 500: 0.80 × 500 = 400. Then 30% of 400: 0.30 × 400 = 120.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: sequential percent-of calculations.
Explanation: Compute 80% of 500: 0.80 × 500 = 400. Then 30% of 400: 0.30 × 400 = 120.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: sequential percent-of calculations.
Q233. A plane travels 480 miles at an average speed of 320 mph. How long does the trip take?
Correct Answer: B
Explanation: Time = distance ÷ speed = 480 ÷ 320 = 1.5 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: time = distance ÷ rate.
Explanation: Time = distance ÷ speed = 480 ÷ 320 = 1.5 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: time = distance ÷ rate.
Q234. A package contains 64 oz of nuts. If 6 oz are unusable, what percent of the nuts are unusable (nearest tenth)?
Correct Answer: B
Explanation: Percent unusable = 6/64 = 0.09375. Convert to percent: 0.09375 × 100 = 9.4%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a whole.
Explanation: Percent unusable = 6/64 = 0.09375. Convert to percent: 0.09375 × 100 = 9.4%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a whole.
Q235. Using π ≈ 3.14, what is the circumference of a circle with a diameter of 14 inches (nearest hundredth)?
Correct Answer: B
Explanation: Circumference = πd = 3.14 × 14 = 43.96 inches.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: circumference of a circle.
Explanation: Circumference = πd = 3.14 × 14 = 43.96 inches.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: circumference of a circle.
Q236. At a deli, 3 sandwiches and 2 drinks cost $31. Two sandwiches and 1 drink cost $19. What is the cost of 1 drink?
Correct Answer: B
Explanation: Let s be sandwich and d be drink. 2s + d = 19 → d = 19 − 2s. Substitute into 3s + 2d = 31: 3s + 2(19 − 2s) = 31 → s = 7. Then d = 19 − 14 = 5.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: system of linear equations.
Explanation: Let s be sandwich and d be drink. 2s + d = 19 → d = 19 − 2s. Substitute into 3s + 2d = 31: 3s + 2(19 − 2s) = 31 → s = 7. Then d = 19 − 14 = 5.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: system of linear equations.
Q237. What is the median of the numbers 4, 7, 9, 12, 15, 18, 21, 22, 27, and 31?
Correct Answer: B
Explanation: There are 10 numbers, so the median is the average of the 5th and 6th values. (15 + 18)/2 = 16.5.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: median for an even-sized data set.
Explanation: There are 10 numbers, so the median is the average of the 5th and 6th values. (15 + 18)/2 = 16.5.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: median for an even-sized data set.
Q238. A 1,000 mL bottle is filled. After 275 mL is used, 18% of what remains is spilled. How many milliliters remain (nearest tenth)?
Correct Answer: B
Explanation: After using 275 mL, remaining is 725 mL. Spilling 18% leaves 82%: 725 × 0.82 = 594.5 mL.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive subtraction and percent decrease.
Explanation: After using 275 mL, remaining is 725 mL. Spilling 18% leaves 82%: 725 × 0.82 = 594.5 mL.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive subtraction and percent decrease.
Q239. A bonus of $960 is split among three employees in a 5:7:12 ratio. How much does the employee with the largest share receive?
Correct Answer: C
Explanation: Total parts = 5 + 7 + 12 = 24. Largest share is 12 parts: 12/24 = 1/2 of the total. 1/2 × 960 = 480.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratio distribution.
Explanation: Total parts = 5 + 7 + 12 = 24. Largest share is 12 parts: 12/24 = 1/2 of the total. 1/2 × 960 = 480.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratio distribution.
Q240. A container holds 1.35 kg of rice and is divided into 18 equal servings. How many grams are in one serving?
Correct Answer: C
Explanation: 1.35 kg = 1,350 g. Divide by 18: 1,350/18 = 75 g per serving.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion and equal partition.
Explanation: 1.35 kg = 1,350 g. Divide by 18: 1,350/18 = 75 g per serving.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion and equal partition.
Q241. A store sells an item for $27.50. If you buy 8 items, you receive 12% off the subtotal (before tax). What is the discounted subtotal?
Correct Answer: B
Explanation: Subtotal = 8 × 27.50 = 220.00. Apply 12% off: 220.00 × 0.88 = $193.60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount on a subtotal.
Explanation: Subtotal = 8 × 27.50 = 220.00. Apply 12% off: 220.00 × 0.88 = $193.60.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount on a subtotal.
Q242. 5/8 of a number is 45. What is the number?
Correct Answer: B
Explanation: If (5/8)x = 45, then x = 45 × (8/5) = 72.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving for an unknown using fractions.
Explanation: If (5/8)x = 45, then x = 45 × (8/5) = 72.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving for an unknown using fractions.
Q243. A boat travels at 18 mph in still water. In a river with a 3 mph current, how long does it take to travel 42 miles upstream?
Correct Answer: B
Explanation: Upstream speed = 18 − 3 = 15 mph. Time = 42 ÷ 15 = 2.8 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: relative rates with current.
Explanation: Upstream speed = 18 − 3 = 15 mph. Time = 42 ÷ 15 = 2.8 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: relative rates with current.
Q244. A salary is $52,000. It increases by 3.5%, and then a $1,200 bonus is added. What is the new total compensation (nearest cent)?
Correct Answer: B
Explanation: After raise: 52,000 × 1.035 = 53,820. Add bonus: 53,820 + 1,200 = $55020.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase plus fixed addition.
Explanation: After raise: 52,000 × 1.035 = 53,820. Add bonus: 53,820 + 1,200 = $55020.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase plus fixed addition.
Q245. A room is 12 ft by 15 ft. Tiles are 12 in by 12 in (1 sq ft each). If 7% extra tiles are needed for cuts and waste, what is the minimum number of tiles to buy?
Correct Answer: C
Explanation: Room area = 12 × 15 = 180 sq ft, so 180 tiles. Add 7% waste: 180 × 1.07 = 192.6, so round up to 193 tiles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area, percent increase, and rounding up.
Explanation: Room area = 12 × 15 = 180 sq ft, so 180 tiles. Add 7% waste: 180 × 1.07 = 192.6, so round up to 193 tiles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area, percent increase, and rounding up.
Q246. A store applies a 20% discount and then a 10% discount on the reduced price. This is equivalent to a single discount of what percent?
Correct Answer: A
Explanation: Successive discounts multiply: price factor = 0.80 × 0.90 = 0.72. Equivalent single discount = 1 − 0.72 = 0.28 = 28%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: equivalent discount from successive percent changes.
Explanation: Successive discounts multiply: price factor = 0.80 × 0.90 = 0.72. Equivalent single discount = 1 − 0.72 = 0.28 = 28%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: equivalent discount from successive percent changes.
Q247. A driver travels 60 miles at 30 mph and then travels another 60 miles at 60 mph. What is the average speed for the entire 120-mile trip?
Correct Answer: B
Explanation: Time out = 60/30 = 2 hours. Time back = 60/60 = 1 hour. Total time = 3 hours. Average speed = 120/3 = 40 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed over equal distances.
Explanation: Time out = 60/30 = 2 hours. Time back = 60/60 = 1 hour. Total time = 3 hours. Average speed = 120/3 = 40 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed over equal distances.
Q248. 18 is 12% of what number?
Correct Answer: C
Explanation: If 0.12 × n = 18, then n = 18 ÷ 0.12 = 150.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: finding the whole from a percent.
Explanation: If 0.12 × n = 18, then n = 18 ÷ 0.12 = 150.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: finding the whole from a percent.
Q249. Three workers produce 18 units in 4 hours at a constant rate per worker. How many units can 5 workers produce in 7 hours at the same rate?
Correct Answer: C
Explanation: Rate per worker-hour = 18 ÷ (3×4) = 1.5 units. With 5 workers for 7 hours: 1.5 × 5 × 7 = 52.5 units.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: scaling output by worker-hours.
Explanation: Rate per worker-hour = 18 ÷ (3×4) = 1.5 units. With 5 workers for 7 hours: 1.5 × 5 × 7 = 52.5 units.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: scaling output by worker-hours.
Q250. A restaurant bill is $86.50. A coupon reduces the bill by 12%, and then an 18% tip is calculated on the discounted bill. What is the total amount paid (nearest cent)?
Correct Answer: A
Explanation: Discounted bill = 86.50 × 0.88 = $76.12. Tip = 0.18 × $76.12 = $13.70. Total = $89.82.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount followed by percent-based tip.
Explanation: Discounted bill = 86.50 × 0.88 = $76.12. Tip = 0.18 × $76.12 = $13.70. Total = $89.82.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount followed by percent-based tip.
Q251. A contractor buys 18 bags of cement at $14.50 each and also pays a flat delivery fee of $38. What is the total cost?
Correct Answer: B
Explanation: Cost of bags = 18 × 14.50 = $261.00. Add delivery fee: $261.00 + $38 = $299.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: total cost with a fixed fee.
Explanation: Cost of bags = 18 × 14.50 = $261.00. Add delivery fee: $261.00 + $38 = $299.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: total cost with a fixed fee.
Q252. A cleaning solution is mixed in a 3:9 ratio of concentrate to water. If you use 3 cups of concentrate, how many cups of solution do you make?
Correct Answer: C
Explanation: A 3:9 ratio means 3 parts concentrate and 9 parts water. With 3 cups concentrate, water is 9 cups. Total solution = 3 + 9 = 12 cups.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratio interpretation and total parts.
Explanation: A 3:9 ratio means 3 parts concentrate and 9 parts water. With 3 cups concentrate, water is 9 cups. Total solution = 3 + 9 = 12 cups.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: ratio interpretation and total parts.
Q253. A salesperson earns a 6% commission on sales. If they sell $8,250 of merchandise, how much commission do they earn (nearest cent)?
Correct Answer: A
Explanation: Commission = 0.06 × 8,250 = $495.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a total.
Explanation: Commission = 0.06 × 8,250 = $495.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent of a total.
Q254. A machine uses 24 gallons of coolant every 6 hours. At the same rate, how many gallons will it use in 90 hours?
Correct Answer: C
Explanation: Rate = 24 gallons per 6 hours = 4 gallons/hour. In 90 hours: 4 × 90 = 360 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate scaling.
Explanation: Rate = 24 gallons per 6 hours = 4 gallons/hour. In 90 hours: 4 × 90 = 360 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate scaling.
Q255. An item sells for $184.80 after being marked up 20% over cost. What was the cost (nearest cent)?
Correct Answer: A
Explanation: Selling price = cost × 1.20, so cost = 184.80 ÷ 1.20 = $154.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent (remove markup).
Explanation: Selling price = cost × 1.20, so cost = 184.80 ÷ 1.20 = $154.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent (remove markup).
Q256. A storage tank holds 240 gallons when full. If 2/5 of the tank is drained, how many gallons remain?
Correct Answer: C
Explanation: Drained amount = (2/5) × 240 = 96. Remaining = 240 − 96 = 144 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a quantity and remainder.
Explanation: Drained amount = (2/5) × 240 = 96. Remaining = 240 − 96 = 144 gallons.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: fraction of a quantity and remainder.
Q257. The average of 6 test scores is 14. If a seventh score of 23 is added, what is the new average (nearest tenth)?
Correct Answer: A
Explanation: Sum of 6 scores = 6 × 14 = 84. New sum = 84 + 23 = 107. New average = 107/7 ≈ 15.3.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Explanation: Sum of 6 scores = 6 × 14 = 84. New sum = 84 + 23 = 107. New average = 107/7 ≈ 15.3.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: averages and totals.
Q258. A rectangular patio is 28 ft by 16 ft. If paving costs $3.25 per square foot, what is the paving cost (nearest cent)?
Correct Answer: A
Explanation: Area = 28 × 16 = 448 sq ft. Cost = 448 × 3.25 = $1456.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area of a rectangle and unit pricing.
Explanation: Area = 28 × 16 = 448 sq ft. Cost = 448 × 3.25 = $1456.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area of a rectangle and unit pricing.
Q259. A jar has 3 red and 2 blue marbles. A coin shows heads with probability 2/7 (a biased coin). If you randomly pick a red marble and then flip the coin once, what is the probability of picking red AND getting heads?
Correct Answer: A
Explanation: Events are independent: P(red) = 3/5 and P(heads) = 2/7. Multiply: (3/5)×(2/7) = 6/35 ≈ 0.171.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: independent probability multiplication.
Explanation: Events are independent: P(red) = 3/5 and P(heads) = 2/7. Multiply: (3/5)×(2/7) = 6/35 ≈ 0.171.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: independent probability multiplication.
Q260. Solve for x: 4x − 9 = 3x + 12.
Correct Answer: D
Explanation: Subtract 3x from both sides: x − 9 = 12. Add 9: x = 21.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving a one-variable linear equation.
Explanation: Subtract 3x from both sides: x − 9 = 12. Add 9: x = 21.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving a one-variable linear equation.
Q261. An employee earns $19.50 per hour and is paid time-and-a-half for hours over 40 in a week. If they work 42 hours, what is the total pay (nearest cent)?
Correct Answer: A
Explanation: Regular pay = 40×19.50 = $780.00. Overtime rate = 1.5×19.50 = $29.25. Overtime pay = 2×$29.25 = $58.50. Total = $838.50.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: wage calculation with overtime rates.
Explanation: Regular pay = 40×19.50 = $780.00. Overtime rate = 1.5×19.50 = $29.25. Overtime pay = 2×$29.25 = $58.50. Total = $838.50.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: wage calculation with overtime rates.
Q262. You have a 12% salt solution and water (0% salt). How many liters of the 12% solution are needed to make 50 liters of an 8% solution (nearest tenth)?
Correct Answer: A
Explanation: Let x be liters of 12% solution. Salt amount = 0.12x. Final salt amount must be 0.08×50 = 4. So 0.12x = 4 → x = 33.3 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture concentration using linear equations.
Explanation: Let x be liters of 12% solution. Salt amount = 0.12x. Final salt amount must be 0.08×50 = 4. So 0.12x = 4 → x = 33.3 L.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: mixture concentration using linear equations.
Q263. A warehouse must pack 725 bolts into boxes that hold 18 bolts each. What is the minimum number of boxes needed?
Correct Answer: C
Explanation: Compute 725 ÷ 18 ≈ 40.28, so you must round up. Minimum boxes = 41.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: division with rounding up to meet capacity.
Explanation: Compute 725 ÷ 18 ≈ 40.28, so you must round up. Minimum boxes = 41.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: division with rounding up to meet capacity.
Q264. A supplier reduces a price of $300 by 15% and later increases the reduced price by 10%. What is the final price (nearest cent)?
Correct Answer: A
Explanation: After 15% decrease: 300×0.85 = 255. After 10% increase: 255×1.10 = $280.50.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent changes.
Explanation: After 15% decrease: 300×0.85 = 255. After 10% increase: 255×1.10 = $280.50.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: successive percent changes.
Q265. A triangle has a perimeter of 44 cm. Two sides measure 13 cm and 17 cm. What is the length of the third side?
Correct Answer: C
Explanation: Perimeter is the sum of all sides. Third side = 44 − 13 − 17 = 14 cm.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: perimeter as a sum of side lengths.
Explanation: Perimeter is the sum of all sides. Third side = 44 − 13 − 17 = 14 cm.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: perimeter as a sum of side lengths.
Q266. A package weighs 7.25 pounds. How many ounces is this? (1 lb = 16 oz)
Correct Answer: C
Explanation: Ounces = 7.25 × 16 = 116 ounces.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion.
Explanation: Ounces = 7.25 × 16 = 116 ounces.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit conversion.
Q267. On a map, 1 inch represents 12 miles. If two towns are 3.75 inches apart on the map, how far apart are they in miles?
Correct Answer: C
Explanation: Use the scale: 3.75 inches × 12 miles per inch = 45 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportions using map scale.
Explanation: Use the scale: 3.75 inches × 12 miles per inch = 45 miles.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportions using map scale.
Q268. A class has 90 students, and 27 of them are in band. What percent of the class is in band?
Correct Answer: C
Explanation: Percent = (27/90) × 100 = 0.3 × 100 = 30%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: part-to-whole percent.
Explanation: Percent = (27/90) × 100 = 0.3 × 100 = 30%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: part-to-whole percent.
Q269. What is the median of the numbers 3, 8, 9, 12, 15, 18, and 22?
Correct Answer: B
Explanation: There are 7 numbers, so the median is the 4th value when ordered. The 4th value is 12.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: median for an odd-sized data set.
Explanation: There are 7 numbers, so the median is the 4th value when ordered. The 4th value is 12.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: median for an odd-sized data set.
Q270. Pipe A fills a tank in 5 hours and Pipe B fills the same tank in 8 hours. If both pipes run together, how long will it take to fill the tank (nearest tenth of an hour)?
Correct Answer: A
Explanation: Combined rate = 1/5 + 1/8 = (8/40 + 5/40) = 13/40 tank per hour. Time = 1 ÷ (13/40) = 40/13 ≈ 3.1 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined work rates.
Explanation: Combined rate = 1/5 + 1/8 = (8/40 + 5/40) = 13/40 tank per hour. Time = 1 ÷ (13/40) = 40/13 ≈ 3.1 hours.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combined work rates.
Q271. A part cost $48 last month and $54 this month. What is the percent increase?
Correct Answer: B
Explanation: Increase = 54 − 48 = 6. Percent increase = 6/48 = 0.125 = 12.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase.
Explanation: Increase = 54 − 48 = 6. Percent increase = 6/48 = 0.125 = 12.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase.
Q272. A loan of $6,000 earns $315 in simple interest at an annual rate of 5.25%. For how many years was the loan outstanding?
Correct Answer: B
Explanation: Using I = Prt: t = I/(Pr) = 315 ÷ (6,000 × 0.0525) = 315 ÷ 315 = 1 year.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (solve for time).
Explanation: Using I = Prt: t = I/(Pr) = 315 ÷ (6,000 × 0.0525) = 315 ÷ 315 = 1 year.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: simple interest (solve for time).
Q273. What is 2 3/4 + 1 5/8?
Correct Answer: C
Explanation: Convert to eighths: 2 3/4 = 2 6/8. Add 1 5/8 → (2+1) and (6/8+5/8) = 3 + 11/8 = 4 3/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: adding mixed numbers with common denominators.
Explanation: Convert to eighths: 2 3/4 = 2 6/8. Add 1 5/8 → (2+1) and (6/8+5/8) = 3 + 11/8 = 4 3/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: adding mixed numbers with common denominators.
Q274. A store sells notebooks for $8.40 each. If you buy 10 or more, you get 10% off the total. What is the total cost for 15 notebooks (nearest cent)?
Correct Answer: B
Explanation: Subtotal = 15 × 8.40 = $126.00. Apply 10% off: multiply by 0.90 → $113.40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount on a subtotal.
Explanation: Subtotal = 15 × 8.40 = $126.00. Apply 10% off: multiply by 0.90 → $113.40.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount on a subtotal.
Q275. Two numbers add to 58. The larger number is 10 more than the smaller. What is the larger number?
Correct Answer: C
Explanation: Let smaller = y and larger = y + 10. Then y + (y + 10) = 58 → 2y = 48 → y = 24. Larger = 24 + 10 = 34.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: translating word statements into linear equations.
Explanation: Let smaller = y and larger = y + 10. Then y + (y + 10) = 58 → 2y = 48 → y = 24. Larger = 24 + 10 = 34.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: translating word statements into linear equations.
Q276. A faucet fills a bucket at 2.5 gallons per minute. How many minutes does it take to fill 18.75 gallons?
Correct Answer: C
Explanation: Time = volume ÷ rate = 18.75 ÷ 2.5 = 7.5 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate = quantity per unit time.
Explanation: Time = volume ÷ rate = 18.75 ÷ 2.5 = 7.5 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: rate = quantity per unit time.
Q277. An account starts with $5,000. First, $800 is withdrawn. Then 25% of the remaining balance is withdrawn. What is the balance after the second withdrawal?
Correct Answer: A
Explanation: After first withdrawal: 5,000 − 800 = 4,200. Withdraw 25% of 4,200: 0.25×4,200 = 1,050. New balance = 4,200 − 1,050 = $3150.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: sequential subtraction and percent-of-remaining.
Explanation: After first withdrawal: 5,000 − 800 = 4,200. Withdraw 25% of 4,200: 0.25×4,200 = 1,050. New balance = 4,200 − 1,050 = $3150.00.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: sequential subtraction and percent-of-remaining.
Q278. Bus A arrives every 12 minutes and Bus B arrives every 18 minutes. If they arrive together at 7:00 AM, when will they next arrive together?
Correct Answer: C
Explanation: They arrive together again after the least common multiple of 12 and 18 minutes. LCM(12,18) = 36, so 7:00 AM + 36 minutes = 7:36 AM.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: least common multiple in scheduling.
Explanation: They arrive together again after the least common multiple of 12 and 18 minutes. LCM(12,18) = 36, so 7:00 AM + 36 minutes = 7:36 AM.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: least common multiple in scheduling.
Q279. Which fraction is equal to 62.5% in simplest form?
Correct Answer: A
Explanation: 62.5% = 0.625 = 625/1000. Simplify: 625/1000 = 5/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent-to-fraction conversion and simplification.
Explanation: 62.5% = 0.625 = 625/1000. Simplify: 625/1000 = 5/8.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent-to-fraction conversion and simplification.
Q280. Using π ≈ 3.14, what is the circumference of a circle with radius 6.5 inches (nearest hundredth)?
Correct Answer: B
Explanation: Circumference = 2πr = 2 × 3.14 × 6.5 = 40.82 inches.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: circumference of a circle.
Explanation: Circumference = 2πr = 2 × 3.14 × 6.5 = 40.82 inches.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: circumference of a circle.
Q281. A driver travels for 1.5 hours at 40 mph and then for 2.5 hours at 55 mph. What is the average speed for the entire trip (nearest tenth)?
Correct Answer: A
Explanation: Distance = 1.5×40 + 2.5×55 = 60 + 137.5 = 197.5 miles. Total time = 4.0 hours. Average speed = 197.5/4.0 = 49.4 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed = total distance ÷ total time.
Explanation: Distance = 1.5×40 + 2.5×55 = 60 + 137.5 = 197.5 miles. Total time = 4.0 hours. Average speed = 197.5/4.0 = 49.4 mph.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: average speed = total distance ÷ total time.
Q282. What is 3/4 of 2/3 of 96?
Correct Answer: C
Explanation: First find 2/3 of 96: 96 ÷ 3 = 32, and 32 × 2 = 64. Then take 3/4 of 64: 64 ÷ 4 = 16, and 16 × 3 = 48.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: multiplying fractions to find a part of a part.
Explanation: First find 2/3 of 96: 96 ÷ 3 = 32, and 32 × 2 = 64. Then take 3/4 of 64: 64 ÷ 4 = 16, and 16 × 3 = 48.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: multiplying fractions to find a part of a part.
Q283. Batteries are sold in a 6-pack for $7.26 and a 10-pack for $11.50. Which pack is cheaper per battery and by how much (nearest cent)?
Correct Answer: C
Explanation: Unit cost (6-pack) = 7.26/6 = $1.21. Unit cost (10-pack) = 11.50/10 = $1.15. The 10-pack is cheaper by about $0.06 per battery.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate comparison.
Explanation: Unit cost (6-pack) = 7.26/6 = $1.21. Unit cost (10-pack) = 11.50/10 = $1.15. The 10-pack is cheaper by about $0.06 per battery.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit rate comparison.
Q284. A service bill includes a 7.5% tax on the base price plus a fixed $4 fee. If the total bill is $52.75, what is the base price (nearest cent)?
Correct Answer: A
Explanation: Let base price be x. Total = 1.075x + 4 = 52.75 → 1.075x = 48.75 → x = 48.75/1.075 = $45.35.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent with an added fixed fee.
Explanation: Let base price be x. Total = 1.075x + 4 = 52.75 → 1.075x = 48.75 → x = 48.75/1.075 = $45.35.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: reverse percent with an added fixed fee.
Q285. A trapezoid has bases of 10 cm and 16 cm and a height of 7 cm. What is its area?
Correct Answer: B
Explanation: Area of a trapezoid = (1/2)(b1 + b2)h = 0.5 × (10 + 16) × 7 = 0.5 × 26 × 7 = 91 cm².
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area of a trapezoid.
Explanation: Area of a trapezoid = (1/2)(b1 + b2)h = 0.5 × (10 + 16) × 7 = 0.5 × 26 × 7 = 91 cm².
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: area of a trapezoid.
Q286. A customer buys 6 items at $19.95 each and receives a 5% member discount. Shipping is free if the discounted subtotal is over $100; otherwise shipping is $12.99. What is the total cost (nearest cent)?
Correct Answer: A
Explanation: Subtotal = 6×19.95 = $119.70. Discounted subtotal = $119.70×0.95 = $113.71. Since $113.71 > $100, shipping is free. Total = $113.71.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount and threshold decision.
Explanation: Subtotal = 6×19.95 = $119.70. Discounted subtotal = $119.70×0.95 = $113.71. Since $113.71 > $100, shipping is free. Total = $113.71.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent discount and threshold decision.
Q287. A recipe uses 2.5 cups of flour to make 14 cookies. How many cups of flour are needed to make 35 cookies at the same rate?
Correct Answer: C
Explanation: Use a proportion: 2.5/14 = x/35. So x = 2.5 × (35/14) = 6.25 cups.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional scaling.
Explanation: Use a proportion: 2.5/14 = x/35. So x = 2.5 × (35/14) = 6.25 cups.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: proportional scaling.
Q288. A store packs 23 items into boxes that hold 6 items each. How many items will be left over after filling as many full boxes as possible?
Correct Answer: C
Explanation: 23 ÷ 6 = 3 remainder 5. After 3 full boxes (18 items), 23 − 18 = 5 items remain.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: division with remainder.
Explanation: 23 ÷ 6 = 3 remainder 5. After 3 full boxes (18 items), 23 − 18 = 5 items remain.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: division with remainder.
Q289. A processing fee is 0.075 of the transaction amount. What is the fee on a $960 transaction?
Correct Answer: C
Explanation: 0.075 = 7.5%. Fee = 0.075 × 960 = 72.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: decimal multiplication and percent equivalence.
Explanation: 0.075 = 7.5%. Fee = 0.075 × 960 = 72.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: decimal multiplication and percent equivalence.
Q290. Group A has 12 people with an average score of 74. Group B has 8 people with an average score of 68. What is the combined average score (nearest tenth)?
Correct Answer: A
Explanation: Total points = 12×74 + 8×68 = 888 + 544 = 1,432. Total people = 20. Combined average = 1,432/20 = 71.6.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average across groups.
Explanation: Total points = 12×74 + 8×68 = 888 + 544 = 1,432. Total people = 20. Combined average = 1,432/20 = 71.6.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: weighted average across groups.
Q291. A buyer has a $250 budget. Each item costs $34, and a 6% tax is applied to the subtotal. What is the maximum number of items the buyer can purchase?
Correct Answer: B
Explanation: Total cost = 34n × 1.06. Compute 34×1.06 = 36.04. Then 250/36.04 ≈ 6.93, so the maximum whole number of items is 6.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: budgeting with tax using inequalities and rounding down.
Explanation: Total cost = 34n × 1.06. Compute 34×1.06 = 36.04. Then 250/36.04 ≈ 6.93, so the maximum whole number of items is 6.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: budgeting with tax using inequalities and rounding down.
Q292. A worker is on the job for 5 hours 20 minutes and takes two 15-minute unpaid breaks. How much time is paid working time?
Correct Answer: B
Explanation: Total time = 5:20 = 320 minutes. Unpaid breaks total 30 minutes. Paid time = 320 − 30 = 290 minutes = 4 hours 50 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: time conversion and subtraction.
Explanation: Total time = 5:20 = 320 minutes. Unpaid breaks total 30 minutes. Paid time = 320 − 30 = 290 minutes = 4 hours 50 minutes.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: time conversion and subtraction.
Q293. A training program’s pass rate rises from 72% to 81%. What is the percent increase relative to the original pass rate?
Correct Answer: B
Explanation: Percent increase relative to original = (81 − 72)/72 = 9/72 = 0.125 = 12.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase relative to a baseline.
Explanation: Percent increase relative to original = (81 − 72)/72 = 9/72 = 0.125 = 12.5%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent increase relative to a baseline.
Q294. An employee’s gross pay is $1,920. Deductions include 12% for tax and 4% for retirement. What is the net pay (nearest cent)?
Correct Answer: A
Explanation: Total deduction percent = 12% + 4% = 16%. Net pay = 1,920 × (1 − 0.16) = 1,920 × 0.84 = $1612.80.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combining percent deductions.
Explanation: Total deduction percent = 12% + 4% = 16%. Net pay = 1,920 × (1 − 0.16) = 1,920 × 0.84 = $1612.80.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: combining percent deductions.
Q295. A rectangular storage box measures 9 ft by 4.5 ft by 2 ft. What is its volume in cubic feet?
Correct Answer: D
Explanation: Volume = length × width × height = 9 × 4.5 × 2. First 9×4.5 = 40.5. Then 40.5×2 = 81.0 cubic feet.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: volume of a rectangular prism.
Explanation: Volume = length × width × height = 9 × 4.5 × 2. First 9×4.5 = 40.5. Then 40.5×2 = 81.0 cubic feet.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: volume of a rectangular prism.
Q296. Gas costs $3.59 per gallon. With a membership discount of $0.05 per gallon, what is the cost to buy 14.8 gallons (nearest cent)?
Correct Answer: A
Explanation: Discounted price per gallon = 3.59 − 0.05 = 3.54. Total cost = 14.8 × 3.54 = $52.39.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit price adjustment and multiplication.
Explanation: Discounted price per gallon = 3.59 − 0.05 = 3.54. Total cost = 14.8 × 3.54 = $52.39.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: unit price adjustment and multiplication.
Q297. A trainee answers 46 questions correctly out of 55. What is the score as a percent (nearest tenth)?
Correct Answer: A
Explanation: Percent = (46/55)×100 ≈ 83.6%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting a fraction to a percent.
Explanation: Percent = (46/55)×100 ≈ 83.6%.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: converting a fraction to a percent.
Q298. A device costs $640. A down payment of 15% is made, and the rest is paid in 8 equal monthly payments. What is the amount of each monthly payment?
Correct Answer: B
Explanation: Down payment = 0.15×640 = 96. Remaining balance = 640 − 96 = 544. Monthly payment = 544 ÷ 8 = 68.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent down payment and equal installment division.
Explanation: Down payment = 0.15×640 = 96. Remaining balance = 640 − 96 = 544. Monthly payment = 544 ÷ 8 = 68.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: percent down payment and equal installment division.
Q299. An item costs $250. A discount of 8% is applied, and then a 6.5% sales tax is added to the discounted price. What is the final price (nearest cent)?
Correct Answer: A
Explanation: Discounted price = 250×0.92 = $230.00. Apply tax: $230.00×1.065 = $244.95.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: discount then tax (successive percent changes).
Explanation: Discounted price = 250×0.92 = $230.00. Apply tax: $230.00×1.065 = $244.95.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: discount then tax (successive percent changes).
Q300. A shopper buys 8 pens and 5 notebooks for a total of $71.50. If each pen costs $4.25, what is the cost of one notebook?
Correct Answer: B
Explanation: Cost of pens = 8×4.25 = $34.00. Remaining amount for notebooks = 71.50 − $34.00 = $37.50. Divide by 5 notebooks: $7.50 each.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving a word problem with totals and unit prices.
Explanation: Cost of pens = 8×4.25 = $34.00. Remaining amount for notebooks = 71.50 − $34.00 = $37.50. Divide by 5 notebooks: $7.50 each.
Citation: ASVAB content domain — Arithmetic Reasoning; underlying principle: solving a word problem with totals and unit prices.
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