ASVAB Study Guide
AR · Practice test 3 of 15

Arithmetic Reasoning Practice Test 3

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AFQT subtest 11 questions No time limit
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  1. Question 1 easy

    If 12 square yards of installed hardwood flooring cost $384, what would be the cost of 30 square yards at the same rate?

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    Correct answer: A — $960

    Find the rate per square yard: $$\frac{384}{12} = 32$$.

    Multiply by 30 square yards: $$32 \times 30 = 960$$

  2. Question 2 easy

    Ryan borrowed some money from his brother. He agreed to pay him back one and a half times the original sum, plus $40. If he paid back a total of $520, what was the original amount Ryan borrowed?

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    Correct answer: B — $320

    Let x be the original amount. Equation: $$1.5x+40=520$$. Subtract 40: $$1.5x=480$$. Divide by 1.5: $$x=320$$

  3. Question 3 easy

    An art broker earned a commission of $7,200, which was 6% of the painting's selling price. What was the selling price of the painting?

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    Correct answer: C — $120,000

    Let S be the selling price. $$0.06 \times S=7{,}200$$. Solve for S: $$S=\frac{7{,}200}{0.06}=120{,}000$$.

  4. Question 4 medium

    A restaurant contains 28 tables, which are a mix of 2-person tables and 4-person tables. If the restaurant can seat a total of 80 people at these tables, how many of the tables are for 2 people?

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    Correct answer: A — 16

    Let x be 2-person tables and y be 4-person tables. $$x+y=28$$ and $$2x+4y=80$$. Substitute $$y=28-x$$: $$2x+4(28-x)=80 \Rightarrow 2x+112-4x=80 \Rightarrow -2x=-32 \Rightarrow x=16$$

  5. Question 5 medium

    A high-end soundbar costs one-eighth the price of a television set without the soundbar. If the combined cost of the television set and the soundbar is $1,080, what is the price of just the soundbar?

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    Correct answer: B — 120

    Let TV price be T. Soundbar is $$(\frac{1}{8})T$$. Total: $$T+(\frac{1}{8})T=1{,}080 \Rightarrow (\frac{9}{8})T=1{,}080 \Rightarrow T=960$$. Soundbar is 1,080 - 960 = $120.

  6. Question 6 medium

    Samantha has a total of $4.50 in dimes and quarters. If she has 4 more quarters than dimes, how many quarters does she have?

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    Correct answer: B — 14

    Let d be dimes and q be quarters ($$q=d+4$$, so $$d=q-4$$). Value: $$0.10d+0.25q=4.50 \Rightarrow 0.10(q-4)+0.25q=4.50 \Rightarrow 0.35q=4.90 \Rightarrow q=14$$

  7. Question 7 medium

    During an 8 weeks summer holiday, the count of sunny days exceeded three times the count of rainy days by 4. How many rainy days occurred?

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    Correct answer: A — 13

    Total days = $$8 \times 7=56$$. Let S be sunny and R be rainy: $$S+R=56$$. We know $$S=3R+4$$. Substitute: $$(3R+4)+R=56 \Rightarrow 4R+4=56 \Rightarrow 4R=52 \Rightarrow R=13$$

  8. Question 8 hard

    Mia received 148 candies in total. If there were 24 fewer chocolates than fruit chews, how many chocolates did she receive?

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    Correct answer: B — 62

    Let C be chocolates and F be fruit chews: $$C+F=148$$ and $$C=F-24 \Rightarrow F=C+24$$. Substitute: $$C+(C+24)=148 \Rightarrow 2C=124 \Rightarrow C=62$$

  9. Question 9 hard

    Given that the ratio of liters to gallons is $$3{,}785:1{,}000$$, how many liters are equivalent to 400 gallons?

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    Correct answer: A — 1,514 liters

    Let L be liters. $$\frac{L}{400}=\frac{3{,}785}{1{,}000}$$. Solve for L: $$L=400 \times 3.785=1{,}514$$ liters.

  10. Question 10 hard

    The interest on a savings bond is determined by the time it is held. If it earns $90 in 6 months, how much will it earn in 2.5 years?

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    Correct answer: B — $450

    Convert 2.5 years to months: $$2.5 \times 12=30$$ months. Rate: $$\frac{90}{6}=15$$ per month. In 30 months: 30 × $15 = $450.

  11. Question 11 hard

    Sarah's motorboat can travel at 12 miles per hour (mph) in still water. She can travel 60 miles downstream in a river in the same amount of time it takes her to travel 36 miles upstream. What is the speed of the river's current?

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    Correct answer: C — 3 mph

    Let c be the current. Downstream speed = $$12 + c$$, Upstream speed $$= 12 - c$$. Since times are equal: $$\frac{60}{(12 + c)} = \frac{36}{(12 - c)} \Rightarrow 60(12 - c) = 36(12 + c) \Rightarrow 720 - 60c = 432 + 36c \Rightarrow 288 = 96c \Rightarrow c = 3$$ mph.