ASVAB Study Guide
AR · Practice test 4 of 15

Arithmetic Reasoning Practice Test 4

Tap an answer to check it instantly and read the explanation. 11 questions: 3 easy, 5 medium and 3 hard.

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  1. Question 1 easy

    Tom packs 4 boxes of supplies every minute, and Jerry packs 3 boxes every minute. If they both work for 15 minutes, what is the total number of boxes they pack together?

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    Correct answer: B — 105

    Combine their packing rates: $$4 + 3 = 7$$ boxes per minute. Multiply by the total time: $$7 \times 15 = 105$$ boxes.

  2. Question 2 easy

    How far will a supply truck go if it travels for 4 hours at a constant speed of 55 miles per hour?

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    Correct answer: A — 220 miles

    Use the formula Distance = Speed × Time. Distance = 55 miles/hour × 4 hours = 220 miles.

  3. Question 3 easy

    Your unit needs to patrol a route across 3.8 grid squares on a military map. If each grid square represents an actual distance of 2,000 meters, what is the total distance, in meters, the unit will patrol?

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    Correct answer: C — 7,600 meters

    Multiply the number of grid squares by the distance per square: $$3.8 \times 2{,}000 = 7{,}600$$ meters.

  4. Question 4 medium

    An investor initially bought $100 worth of crypto assets. The asset value decreased by 20% in the first month and then increased by 20% in the second month. What is the current value of the asset?

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    Correct answer: B — $96

    First month value: $100 × (1 - 0.20) = $80. Second month value: $80 × (1 + 0.20) = $96.00.

  5. Question 5 medium

    Mark can build a brick wall in 40 hours working alone. If he works with his three apprentices, and each of them works 8 hours per day at the same pace as Mark, how many days will it take the entire team to complete the wall?

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    Correct answer: A — 1.25

    Total workload: 40 man-hours.

    Team productivity (4 people): $$4 \times 8 = 32$$ man-hours/day. Number of days to complete: $$\frac{40}{32} = 1.25$$ days.

  6. Question 6 medium

    Over a period of five days, Sarah reads a total of 150 pages of a book. Each day, she reads five more pages than she read the day before. How many pages did Sarah read on the first day?

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    Correct answer: B — 20

    Let x be the number of pages read on the first day. The sequence for 5 days is: x, $$x+5$$, $$x+10$$, $$x+15$$, and $$x+20$$. Their sum is: $$x + (x+5) + (x+10) + (x+15) + (x+20) = 150$$. Simplifying, we get $$5x + 50 = 150$$. Subtract 50 from both sides: $$5x = 100$$. Divide by 5: $$x = 20$$

  7. Question 7 medium

    A pancake recipe yields 6 servings at 250 calories per serving. If you prepare 125% of the recipe's quantity instead of the original 100%, what is the total calorie count of your batch?

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    Correct answer: C — 1875

    First, calculate the total calories of the original recipe: 6 servings × 250 calories/serving = 1,500 calories. Next, find 125% of this total quantity: $$1{,}500 \times 1.25 = 1{,}875$$ calories.

  8. Question 8 medium

    Emma's age is four times Liam's age. If their combined age is 35, how old is Liam?

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    Correct answer: B — 7

    Let L be Liam's age. Emma's age is $$4L$$. Their combined age is $$L + 4L = 35$$. This simplifies to $$5L = 35$$. Dividing both sides by 5 gives $$L = 7$$

  9. Question 9 hard

    A freight train leaves its station and travels towards the city at an average rate of 60 km per hour. Two hours later, a passenger train leaves from the same station on a parallel track traveling at an average rate of 90 km per hour. How many hours will it take the passenger train to overtake the freight train?

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    Correct answer: B — 4 hours

    Let t be the time the passenger train travels. The freight train travels for $$(t + 2)$$ hours. When they meet, their distances are equal: $$60(t + 2) = 90t$$. Expanding this: $$60t + 120 = 90t$$. Subtract $$60t$$ from both sides: $$120 = 30t$$. Divide by 30: $$t = 4$$ hours.

  10. Question 10 hard

    A wallet containing $42 consists only of $1 bills and $5 bills. If the number of $1 bills is twice the number of $5 bills, how many of each bill are in the wallet?

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    Correct answer: B — 12 $1 bills and 6 $5 bills

    Let F be the number of $5 bills. The number of $1 bills is $$2F$$. The total value is $42, so $$1 \times (2F) + 5 \times (F) = 42$$. This simplifies to $$2F + 5F = 42$$, meaning $$7F = 42$$. So, $$F = 6$$. The number of $1 bills is $$2 \times (6) = 12$$

  11. Question 11 hard

    Given the equation $$3x^2 = 108$$, determine the possible values of x.

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    Correct answer: D — ±6

    First, isolate x² by dividing both sides by 3: $$x^2 = \frac{108}{3}$$,

    which gives $$x^2 = 36$$.

    Taking the square root of both sides gives $$x = \pm 6$$ (both positive and negative 6 are valid roots).