ASVAB Arithmetic Reasoning Practice Test 14

Question 1 easy

Farmer Al is selling his 250-acre orchard at $4,000 per acre. He's giving the buyer $100,000 worth of land. What fraction of his total land is he giving to the buyer?

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Correct answer: B — $$\frac{1}{10}$$

First, calculate the total value of the farm: 250 acres × $4,000/acre = $1,000,000. Next, find the fraction given to the buyer: $$\frac{100{,}000}{1{,}000{,}000} = \frac{1}{10}$$. Therefore, the fraction of his total land is $$\frac{1}{10}$$

Question 2 easy

Mr. Davis bought a watch for $50 and sold it for $65. What is the percentage increase in the price?

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Correct answer: C — 30

The increase in price is $65 - $50 = $15. To find the percentage increase, divide the increase by the original price and multiply by 100: $$(\frac{15}{50}) \times 100 = 0.3 \times 100 = 30\%$$.

Question 3 easy

On a map where 1 inch represents 4 miles, the distance between Town A and Town B is $$145 \frac{1}{2}$$ inches. What is the total distance, in miles, for a round trip between the two towns?

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Correct answer: B — 1,164 miles

First, calculate the total distance of the round trip in inches: $$145.5\text{ inches} \times 2 = 291$$ inches. Since 1 inch represents 4 miles, convert the distance to miles: $$291 \times 4 = 1{,}164$$ miles.

Question 4 medium

A college student spends $$\frac{1}{3}$$ of their day sleeping, $$\frac{1}{12}$$ eating, $$\frac{1}{8}$$ traveling, and $$\frac{3}{8}$$ studying and in class. How many hours per day are left for discretionary time?

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Correct answer: A — 2 hours

First, find the sum of the fractions of the day spent: $$\frac{1}{3} + \frac{1}{12} + \frac{1}{8} + \frac{3}{8}$$. Find a common denominator, which is 24: $$\frac{8}{24}$$ (sleeping) + $$\frac{2}{24}$$ (eating) + $$\frac{3}{24}$$ (traveling) + $$\frac{9}{24}$$ (studying) $$= \frac{22}{24} = \frac{11}{12}$$. The remaining fraction of the day is $$1 - \frac{11}{12} = \frac{1}{12}$$. Since a day has 24 hours, the left-over hours $$= 24 \times (\frac{1}{12}) = 2$$ hours.

Question 5 medium

A leather jacket costs $240.00 at a high-end boutique and $192.00 at an online wholesale store. What is the percentage increase in price when buying from the boutique?

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Correct answer: B — The boutique's jacket costs 25% more than the wholesale jacket.

The percentage increase is calculated relative to the wholesale price: Increase = $240.00 - $192.00 = $48.00. Percentage Increase = $$(\frac{48.00}{192.00}) \times 100 = 0.25 \times 100 = 25\%$$. Therefore, the boutique's jacket costs 25% more than the wholesale jacket.

Question 6 medium

Six employees completed a training program in the following number of hours: 14, 18, 11, 15, 22, and 19. What is the median number of hours to complete the program?

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Correct answer: D — 16.5 hours

To find the median, first arrange the numbers in ascending order: 11, 14, 15, 18, 19, 22. Since there is an even number of values (6), find the mean of the two middle numbers (15 and 18): $$\frac{(15 + 18)}{2} = 16.5$$ hours.

Question 7 medium

A baker baked 150 croissants in the morning and sold 120 of them by noon. What percentage of the croissants remains unsold?

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Correct answer: A — 20%

First, calculate the number of remaining croissants: $$150 - 120 = 30$$. Then, calculate the remaining percentage: $$(\frac{30}{150}) \times 100\% = 20\%$$

Question 8 hard

Jack can clean the office building in 36 hours. If his 2 coworkers help, each working 6 hours a day, how many days will it take them all to finish the job, assuming everyone works at the same pace?

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Correct answer: B — 2 days

Jack alone takes 36 hours, meaning the job requires 36 total worker-hours. With 2 coworkers helping, there are 3 workers in total (Jack + 2 coworkers). Since they each work 6 hours a day, the combined work rate per day is: 3 workers × 6 hours/day = 18 worker-hours/day. Therefore, the number of days needed is: 36 worker-hours / 18 worker-hours/day = 2 days.

Question 9 hard

Emma purchases a winter coat for $102.00, which is at a 15% discount from the original price. If the coat were discounted 30% from the original price instead, what would the sale price have been?

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Correct answer: B — $84

The $102.00 purchase price represents 85% of the original price $$(100\% - 15\%)$$. First, find the original price: $$\frac{102.00}{0.85} = 120.00$$. Now, apply a 30% discount to this original price (which means paying 70% of the original price): Final sale price = $120.00 × 0.70 = $84.00.

Question 10 hard

Sophia spent $68 on 4 tickets to a local museum and a $20 guidebook. What is the cost of one museum ticket?

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Correct answer: B — $12

Subtract the cost of the guidebook from the total money spent to find the total cost of the tickets: $68 - $20 = $48. Divide the remaining amount by the number of tickets to find the price per ticket: $$\frac{48}{4}$$ tickets = $12.00 per ticket.

Question 11 hard

Leo spends $120 on organic coffee beans at a roastery where the minimum order is 15 bags. The coffee is priced at $6.00 per bag. How many bags did Leo buy above the minimum order requirement?

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Correct answer: A — 5 bags

First, find the total number of bags Leo bought by dividing his total spending by the cost per bag: $$\frac{120}{6.00} = 20$$ bags. Since the minimum order is 15 bags, the number of bags bought above this requirement is: 20 bags - 15 bags = 5 bags.