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ASVAB · Arithmetic Reasoning · Topic Study Guide

Word Problems: Practice Questions & Explanations

7 Arithmetic Reasoning questions on word problems, each with a worked explanation citing the source handbook.

Source: ASVAB official content outline and Department of Defense study guides (public domain).

Reviewed by Jordan Morley, Editorial Lead at 247SimpleTests. Written by the 247SimpleTests Editorial Team from the official source material cited on every question.

Why this topic matters

Arithmetic Reasoning is almost entirely word problems: the maths is basic, the skill is translating a sentence into an operation — rate × time, part of a whole, unit price, remaining amount. Read for the question being asked, write the setup before calculating, and sanity-check the answer against the choices.

Below are every word problem question in our Arithmetic Reasoning bank. Read each question, try to answer before reading the explanation, and use the source citations to look up anything you want to verify.

1. A car travels 240 miles on 8 gallons of gas. How many miles per gallon does it get?
  1. A 28 mpg
  2. B 26 mpg
  3. C 30 mpg
  4. D 32 mpg

Explanation

MILES PER GALLON = total miles ÷ gallons used = 240 ÷ 8 = 30 mpg. ASVAB Arithmetic Reasoning tests rate/word problems. 'Per gallon' signals division (miles divided by gallons). Set it up as a unit rate: 240 miles / 8 gallons = 30 miles/gallon. Strategy: identify what's being asked (a rate, 'per' something), then divide the total by the number of units. Check: 30 mpg × 8 gallons = 240 miles. ✓
Source: ASVAB Arithmetic Reasoning — Rate Problems

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2. If 5 workers can build a wall in 12 days, how long would it take 10 workers (working at the same rate)?
  1. A 24 days
  2. B 10 days
  3. C 8 days
  4. D 6 days

Explanation

This is an INVERSE proportion — more workers means LESS time. Total work = 5 workers × 12 days = 60 worker-days. With 10 workers: 60 ÷ 10 = 6 days. ASVAB Arithmetic Reasoning tests work-rate problems.

Key insight: doubling the workers (5 to 10) halves the time (12 to 6 days). Strategy: for inverse relationships, find the total 'work' (workers × time), then divide by the new number of workers. Watch for the inverse relationship — more workers/machines = less time, not more.

Source: ASVAB Arithmetic Reasoning — Work Rate (Inverse)

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3. A store buys an item for $60 and sells it for $75. What is the percent markup?
  1. A 20%
  2. B 25%
  3. C 30%
  4. D 15%

Explanation

PERCENT MARKUP = (increase ÷ original cost) × 100. The increase is $75 − $60 = $15. Markup = (15 ÷ 60) × 100 = 0.25 × 100 = 25%. ASVAB Arithmetic Reasoning tests percent change. Strategy: percent increase/markup is always based on the ORIGINAL (cost) amount, not the new price. Find the difference ($15), divide by the original ($60), and convert to a percent. Note: this differs from percent of profit based on selling price — markup uses cost as the base.
Source: ASVAB Arithmetic Reasoning — Percent Markup

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4. Three people split a restaurant bill of $90 equally, then add a $18 tip split equally. How much does each person pay in total?
  1. A $30
  2. B $36
  3. C $38
  4. D $34

Explanation

Total to split = bill + tip = $90 + $18 = $108. Split among 3 people: $108 ÷ 3 = $36 each. ASVAB Arithmetic Reasoning tests multi-step word problems.

Alternate: split each part separately — bill: $90 ÷ 3 = $30; tip: $18 ÷ 3 = $6; total per person: $30 + $6 = $36. Both methods give $36. Strategy: for multi-step problems, you can combine amounts first then divide, or divide each part then add — choose whichever is clearer. Check: $36 × 3 = $108 = $90 + $18. ✓

Source: ASVAB Arithmetic Reasoning — Multi-Step Problems

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5. A train leaves at 2:00 PM traveling at 60 mph. How far has it traveled by 5:30 PM?
  1. A 195 miles
  2. B 210 miles
  3. C 180 miles
  4. D 240 miles

Explanation

DISTANCE = rate × time. Time elapsed from 2:00 PM to 5:30 PM = 3.5 hours. Distance = 60 mph × 3.5 hours = 210 miles. ASVAB Arithmetic Reasoning tests distance-rate-time problems (d = r × t). Strategy: carefully calculate the time (3 hours 30 minutes = 3.5 hours, NOT 3.3), then multiply by the rate. Common error: writing 30 minutes as 0.30 instead of 0.5 hour. Half an hour = 0.5. Check: 60 × 3 = 180, plus 60 × 0.5 = 30, total 210. ✓
Source: ASVAB Arithmetic Reasoning — Distance-Rate-Time

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6. A jacket is marked down 20%, then an additional 10% is taken off the sale price. If the original price was $100, what is the final price?
  1. A $72
  2. B $75
  3. C $68
  4. D $70

Explanation

Successive discounts must be applied ONE AT A TIME (not added together). First discount: 20% off $100 → pay 80% → 0.80 × $100 = $80. Second discount: 10% off $80 → pay 90% → 0.90 × $80 = $72. ASVAB Arithmetic Reasoning tests successive percentages.

Common error: adding 20% + 10% = 30% off ($70) is WRONG — the second discount applies to the already-reduced price. Strategy: apply each discount sequentially. The final price is $72, not $70.

Source: ASVAB Arithmetic Reasoning — Successive Discounts

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7. If a 15% tip on a meal is $9, what was the cost of the meal?
  1. A $45
  2. B $72
  3. C $54
  4. D $60

Explanation

If 15% of the meal = $9, then the meal cost = $9 ÷ 0.15 = $60. ASVAB Arithmetic Reasoning tests working backward from a percentage. Set up: 0.15 × (meal) = $9, so meal = 9 ÷ 0.15 = $60. Strategy: when given the result of a percentage and asked for the original, DIVIDE by the decimal form of the percentage. Check: 15% of $60 = 0.15 × 60 = $9. ✓ Common error: multiplying instead of dividing — remember you're finding the larger whole from a part.
Source: ASVAB Arithmetic Reasoning — Working Backward from Percent

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