ASVAB Arithmetic Reasoning Practice Test 15

Question 1 easy

Each car requires 4 hours for one mechanic to assemble. If a garage needs to assemble 24 cars in 8 hours, how many mechanics must work on the cars?

Show answer & explanation

Correct answer: B — 12

To assemble 24 cars, with each car taking 4 mechanic-hours, the total labor hours needed is:

24 cars × 4 hours/car = 96 mechanic-hours.

Since the assembly must be completed in 8 hours, the number of mechanics required is: 96 hours / 8 hours = 12 mechanics.

Question 2 easy

A bag contains 5 blue, 4 yellow, and 3 green marbles. If Sarah takes out one green marble and does not replace it, what is the probability that the next marble she randomly draws will also be green?

Show answer & explanation

Correct answer: A — $$\frac{2}{11}$$

Initially, there are 12 marbles (5 blue + 4 yellow + 3 green). After Sarah removes 1 green marble without replacing it, there are now only 11 marbles left in total, and only 2 of them are green. Thus, the probability of drawing another green marble is 2 out of $$11 (\frac{2}{11})$$

Question 3 easy

A jar contains 5 red jellybeans and 5 blue jellybeans. If two jellybeans are selected at random without replacement, what is the probability that both selected jellybeans are red?

Show answer & explanation

Correct answer: B — 2 in 9

There are 10 jellybeans in total initially. The probability of selecting a red jellybean first is $$\frac{5}{10}$$. Since the selection is without replacement, there are now 9 jellybeans left, 4 of which are red. The probability of selecting a second red jellybean is $$\frac{4}{9}$$. The combined probability is $$(\frac{5}{10}) \times (\frac{4}{9}) = \frac{20}{90} = \frac{2}{9}$$ (or 2 in 9).

Question 4 medium

David inherited $40,000. He invested a portion of it in a savings account earning 6% interest annually, and the rest in a mutual fund earning 9% interest annually. If his total annual interest from both investments is $3,150, how much did he invest at 9%?

Show answer & explanation

Correct answer: B — $25,000

Let x be the amount invested at 9%. The remaining amount invested at 6% is $$(40{,}000 - x)$$. Set up the annual interest equation: $$0.09x + 0.06(40{,}000 - x) = 3{,}150$$. Simplify the equation: $$0.09x + 2{,}400 - 0.06x = 3{,}150 \Rightarrow 0.03x = 750 \Rightarrow x = 25{,}000$$. Thus, David invested $25,000 at 9%.

Question 5 medium

Mr. Smith is 24 years older than his son. In 10 years, Mr. Smith's age will be double his son's age. What is Mr. Smith's current age?

Show answer & explanation

Correct answer: B — 38

Let S be the son's current age. Mr. Smith's current age is $$S + 24$$. In 10 years, their ages will be $$(S + 10)$$ and $$(S + 34)$$ respectively. According to the problem: $$S + 34 = 2 \times (S + 10) \Rightarrow S + 34 = 2S + 20 \Rightarrow S = 14$$. Therefore, Mr. Smith's current age is $$14 + 24 = 38$$ years.

Question 6 medium

Sarah started a catering business. In her first month, she had $450 in ingredient costs, drove 600 miles at $0.35 per mile, and had $150 in kitchen rentals. She completed 45 catering orders at $60 each. What was her profit for the month?

Show answer & explanation

Correct answer: B — $1,890

First, calculate her total revenue: 45 orders × $60/order = $2,700. Next, calculate her expenses: Ingredients ($450) + Mileage ($$600\text{ miles} \times 0.35 = 210$$) + Kitchen rental ($150) = $810. Profit = Revenue - Expenses = $2,700 - $810 = $1,890.

Question 7 medium

Alex and Brian are selling their coffee shop for $180,000. They want to split the money based on their investment ratio. Alex invested more, with a $$5:3$$ ratio compared to Brian's investment. How much of the money should Brian receive?

Show answer & explanation

Correct answer: A — $67,500

The total investment ratio parts are $$5 + 3 = 8$$ parts. Brian's fraction of the investment is $$\frac{3}{8}$$. Therefore, Brian should receive: $$(\frac{3}{8}) \times 180{,}000 = 67{,}500$$.

Question 8 hard

Chloe purchases a $28,000 car with a four-year loan at a simple interest rate of 5.5%. What is the total amount she will pay, including both the principal and the interest, by the end of the loan term?

Show answer & explanation

Correct answer: A — $34,160

The simple interest formula is $$I = P \times r \times t$$. Here, $$P = 28{,}000$$, $$r = 0.055$$, and $$t = 4$$ years. Interest $$(I) = 28{,}000 \times 0.055 \times 4 = 6{,}160$$. The total amount paid is Principal + Interest = $28,000 + $6,160 = $34,160.

Question 9 hard

Henry received a water bill of $78.45 for August. This bill includes a fixed monthly service charge of $25.00 and an additional charge of $0.11 for each hundred gallons (hgal) of water consumed. Approximately what quantity of hgal did Henry use during August?

Show answer & explanation

Correct answer: A — 485.91

Subtract the fixed monthly charge from the total bill: $78.45 - $25.00 = $53.45. Next, divide this remaining amount by the cost per hundred gallons: $$\frac{53.45}{0.11} \approx 485.91$$ hgal.

Question 10 hard

Liam earns simple interest on a fixed amount of money. If the investment earns $90 in 6 months, how much will it earn in 2.5 years?

Show answer & explanation

Correct answer: B — $450

First, find the earnings per month: $$\frac{90}{6}$$ months = $15 per month. Convert 2.5 years into months: $$2.5 \times 12 = 30$$ months. Total interest earned in 30 months = 30 × $15 = $450.

Question 11 hard

If a designer bag originally costs $400, and it is discounted by 20% and then by another 10%, what is the final price?

Show answer & explanation

Correct answer: B — $288

First discount of 20%: Price becomes $400 × (1 - 0.20) = $400 × 0.80 = $320. Second discount of 10% applied to the new price: Final price = $320 × (1 - 0.10) = $320 × 0.90 = $288.