ASVAB Arithmetic Reasoning Practice Test 3: Percents, Ratios and Unit Rates
- Percents, Ratios and Unit Rates
- 10 questions
- 15 minutes
These word problems focus on percents, ratios and comparing prices or rates. Before you calculate, decide what the question asks for: a part, a whole or a change.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A platoon has 40 soldiers, and 35% of them are women. How many soldiers in the platoon are men?
Correct answer: B
If 35% are women, 65% are men: 0.65 × 40 = 26. The answer 14 is the number of women, not men.
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Question 2
In a motor pool, the ratio of trucks to jeeps is 5 : 3. There are 24 more trucks than jeeps. How many trucks and jeeps are there in all?
Correct answer: D
The difference of 5 − 3 = 2 parts equals 24 vehicles, so one part is 12. The total is 8 parts: 8 × 12 = 96. The answer 60 counts only the trucks.
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Question 3
A store raises the price of an $80 jacket by 25%. Later it lowers the new price by 25%. What is the final price?
Correct answer: A
After the raise the price is $80 × 1.25 = $100. A 25% cut of $100 is $25, leaving $75. The two changes do not cancel because the second 25% is taken from a larger price.
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Question 4
A recruit runs 3 miles in 24 minutes. At the same pace, how many minutes will it take to run 5 miles?
Correct answer: C
The pace is 24 ÷ 3 = 8 minutes per mile, so 5 miles take 5 × 8 = 40 minutes.
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Question 5
The number 18 is 24% of what number?
Correct answer: A
Divide the part by the percent: 18 ÷ 0.24 = 75. The answer 4.32 comes from multiplying 18 by 0.24, which finds 24% of 18 instead.
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Question 6
A 12-pack of water costs $9.00 and an 18-pack costs $12.60. Which is the better buy per bottle, and by how much?
Correct answer: D
The 12-pack costs $9.00 ÷ 12 = $0.75 per bottle and the 18-pack costs $12.60 ÷ 18 = $0.70 per bottle, so the 18-pack is cheaper by $0.05.
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Question 7
A sales tax of 6% is added to a $45.00 purchase. What is the total cost?
Correct answer: B
The tax is 0.06 × $45.00 = $2.70, so the total is $45.00 + $2.70 = $47.70.
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Question 8
The population of a small town grew from 12,000 to 15,000. By what percent did the population increase?
Correct answer: C
The increase is 3,000. Compare it with the original population: 3,000 ÷ 12,000 = 0.25 = 25%. Dividing by the new population, 15,000, gives the wrong answer 20%.
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Question 9
Concrete is mixed from cement, sand and gravel in the ratio 1 : 2 : 4 by volume. How many cubic feet of sand are needed for 21 cubic feet of concrete mix?
Correct answer: A
The ratio has 1 + 2 + 4 = 7 parts, so one part is 21 ÷ 7 = 3 cubic feet. Sand is 2 parts: 2 × 3 = 6 cubic feet. The answer 12 is the gravel.
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Question 10
A water tank is 40% full. After 18 gallons are added, it is 70% full. How many gallons does the tank hold when it is completely full?
Correct answer: B
The 18 gallons raised the level by 70% − 40% = 30% of the tank. If 30% is 18 gallons, the full tank is 18 ÷ 0.30 = 60 gallons.
Questions you leave blank are not counted as wrong.
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