ASVAB Arithmetic Reasoning Practice Test 5 – 11 Questions with Answers

Question 1 easy

David travels 40 miles per hour going to his office and 30 miles per hour coming back along the exact same route. If he drives for a total of 7 hours, what is the distance from his home to his office, rounded to the nearest mile?

Show answer & explanation

Correct answer: C — 120

Let d be the distance.

Time going = $$\frac{d}{40}$$, Time returning $$= \frac{d}{30}$$. Total time: $$\frac{d}{40} + \frac{d}{30} = 7 \Rightarrow \frac{(3d + 4d)}{120} = 7 \Rightarrow 7d/120 = 7 \Rightarrow d = 120$$ miles.

Question 2 easy

Sarah obtains a four-year business loan of $25,000 at a simple interest rate of 7.5% per year. What is the total amount she pays over the life of the loan, including both the principal and the interest?

Show answer & explanation

Correct answer: A — 32,500

Calculate simple interest: $$I = \text{Principal} \times \text{Rate} \times \text{Time} = 25{,}000 \times 0.075 \times 4 = 7{,}500$$. Total amount = $25,000 + $7,500 = $32,500.

Question 3 easy

Given that 3 jackets, 3 pairs of boots, and 1 hat cost $390, and 7 jackets, 7 pairs of boots, and 3 hats cost $950, find the combined cost of 1 jacket, 1 pair of boots, and 1 hat?

Show answer & explanation

Correct answer: B — 170

Let (jacket + boot) = X and hat = Y. Equation 1: $$3X + Y = 390 \Rightarrow Y = 390 - 3X$$. Equation 2: $$7X + 3Y = 950$$. Substitute Y: $$7X + 3(390 - 3X) = 950 \Rightarrow 7X + 1170 - 9X = 950 \Rightarrow -2X = -220 \Rightarrow X = 110$$. Since $$X = 110$$, $$Y = 390 - 3(110) = 60$$. Combined cost of 1 jacket, 1 pair of boots, and 1 hat $$(X + Y) = 110 + 60 = 170$$

Question 4 medium

Alex's incorrect answers on a test were 8 less than his total questions. If $$\frac{3}{5}$$ of his total questions equaled 3 times his incorrect answers, what was the total number of questions on the test?

Show answer & explanation

Correct answer: A — 10

Let Q be the total questions and W be the incorrect answers. We have $$W = Q - 8 \Rightarrow Q - W = 8$$. Also, $$(\frac{3}{5})Q = 3W \Rightarrow Q = 5W$$. Substitute Q into the first equation: $$5W - W = 8 \Rightarrow 4W = 8 \Rightarrow W = 2$$. Therefore, $$Q = 5 \times 2 = 10$$

Question 5 medium

A delivery truck left Chicago at 8 a.m. At 10 a.m., a motorcycle left from the same spot, going 15 miles per hour faster than the truck. It caught up with the truck at 2 p.m. How many miles from Chicago did the motorcycle overtake the truck?

Show answer & explanation

Correct answer: B — 180

Truck time from 8 a.m. to 2 p.m. = 6 hours. Motorcycle time from 10 a.m. to 2 p.m. = 4 hours. Let v be the speed of the truck. Motorcycle speed is $$v + 15$$. Distance is equal: $$6v = 4(v + 15) \Rightarrow 6v = 4v + 60 \Rightarrow 2v = 60 \Rightarrow v = 30$$ mph. Overtaking distance $$= 6 \times 30 = 180$$ miles.

Question 6 medium

Two pipes are used to fill a water tank. Pipe A requires 10 hours to fill the tank alone, while Pipe B requires 15 hours. How long would it take for both pipes working together to fill the tank?

Show answer & explanation

Correct answer: B — 6 hours

Let the rate of Pipe A be $$\frac{1}{10}$$ and Pipe B be $$\frac{1}{15}$$. Combined rate $$= \frac{1}{10} + \frac{1}{15} = \frac{(3 + 2)}{30} = \frac{5}{30} = \frac{1}{6}$$. Therefore, the time taken for both working together is 6 hours.

Question 7 medium

Mr. Jenkins sold a collector's book for $24, incurring a percentage loss equal to the book's original cost in dollars. What was the original cost of the book?

Show answer & explanation

Correct answer: C — $40

Let C be the original cost. Loss percent = C%, so actual loss in dollars = $$C \times (\frac{C}{100}) = \frac{C^2}{100}$$. Selling Price = Cost - Loss => $$24 = C - \frac{C^2}{100}$$. Rearranging gives: $$C^2 - 100C + 2400 = 0 \Rightarrow (C - 60)(C - 40) = 0$$. Thus, C can be $60 or $40. Only $40 is among the choices.

Question 8 medium

During a road trip, Sophia and Ethan drove for 3 hours, stopped for gas, and then drove 180 miles in 2 hours. If their average driving speed for the entire trip was 64 miles per hour, how many miles did they travel before stopping for gas?

Show answer & explanation

Correct answer: B — 140 miles

Total driving time = $$3 + 2 = 5$$ hours. With an average driving speed of 64 mph, total distance $$= 5 \times 64 = 320$$ miles. Since the distance after the gas stop was 180 miles, the distance before the stop was $$320 - 180 = 140$$ miles.

Question 9 hard

Consider three consecutive odd integers. If the sum of the first and the third is 151 less than three times the second, what is the first of these integers?

Show answer & explanation

Correct answer: D — 149

Let the integers be $$x$$, $$x+2$$, $$x+4$$. Then $$2x + 4 = 3(x+2) - 151 \Rightarrow 2x + 4 = 3x - 145 \Rightarrow x = 149$$.

Question 10 hard

A cyclist rides up a mountain pass at 12 mph and down the exact same pass at 20 mph. If the entire round trip takes 8 hours of riding, what is the distance of the pass (one way) rounded to the nearest mile?

Show answer & explanation

Correct answer: A — 60 miles

Let d be the one-way distance. Time up = $$\frac{d}{12}$$, Time down $$= \frac{d}{20}$$. Total time: $$\frac{d}{12} + \frac{d}{20} = 8 \Rightarrow \frac{(5d + 3d)}{60} = 8 \Rightarrow 8d/60 = 8 \Rightarrow 8d = 480 \Rightarrow d = 60$$ miles.

Question 11 hard

A boutique sells 3 dresses, 3 designer bags, and 1 scarf for a total of $350. If a dress costs double a scarf, and a bag costs $50 more than a scarf, what is the combined cost of one dress, one bag, and one scarf?

Show answer & explanation

Correct answer: B — $130

Let Scarf = S. Then Dress = $$2S$$ and Bag $$= S + 50$$. Equation: $$3(2S) + 3(S + 50) + S = 350 \Rightarrow 10S + 150 = 350 \Rightarrow 10S = 200 \Rightarrow S = 20$$. So Scarf = $20, Dress = $40, Bag = $70. Combined cost of one dress, one bag, and one scarf = 40 + 20 + 70 = $130.