ASVAB Study GuideArithmetic Reasoning Practice Test 6
Tap an answer to check it instantly and read the explanation. 11 questions: 3 easy, 5 medium and 3 hard.
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Question 1 easy
A 6-foot lamppost casts a 3-foot shadow on the ground. At the exact same time, a nearby flagpole casts an 18-foot shadow. How tall is the flagpole?
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Correct answer: B — 36 feet
The ratio of height to shadow is constant for objects nearby at the same time:
Height/Shadow = $$\frac{6}{3} = 2$$.
Let H be the height of the flagpole: $$\frac{H}{18} = 2 \Rightarrow H = 36$$ feet.
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Question 2 easy
Chloe wants to lay hardwood flooring in her living room, which measures 15 feet in length and 12 feet in width. What is the total area of flooring she needs to purchase?
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Correct answer: A — 180 square feet
The area of a rectangle is calculated by multiplying the length by the width: Area = Length × Width = 15 feet × 12 feet = 180 square feet.
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Question 3 easy
A rectangular backyard swimming pool has a perimeter of 120 feet and a length of 40 feet. What is the width of the swimming pool?
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Correct answer: B — 20 feet
The formula for the perimeter of a rectangle is $$P = 2(L + W)$$. Given $$P = 120$$ and $$L = 40$$: $$120 = 2(40 + W) \Rightarrow 60 = 40 + W \Rightarrow W = 20$$ feet.
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Question 4 medium
A square-shaped community garden has an area of 144 square feet. What is the length of one of its sides?
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Correct answer: C — 12 feet
The area of a square is given by $$\text{Side}^2$$. Therefore, the length of one side is the square root of the area: Side $$= \sqrt{144} = 12$$ feet.
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Question 5 medium
In a right triangle with one leg measuring 5 and the other leg measuring 12, what is the length of the hypotenuse?
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Correct answer: A — 13
According to the Pythagorean theorem, the hypotenuse c of a right triangle with legs a and b is given by $$c = \sqrt{a^2 + b^2}$$. Here, $$c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$$
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Question 6 medium
A rectangle has a length of 12 inches and a width of 8 inches. What is its area?
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Correct answer: C — 96 square inches
The area of a rectangle is found by multiplying its length by its width: Area = Length × Width = 12 inches × 8 inches = 96 square inches.
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Question 7 medium
A storage container has the shape of a cube, with each of its edges measuring 6 inches. What is the volume of this container?
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Correct answer: B — 216 cubic inches
The volume of a cube is calculated using the formula $$V = s^3$$, where s is the length of an edge: Volume $$= 6^3 = 6 \times 6 \times 6 = 216$$ cubic inches.
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Question 8 medium
Liam needs to fence a triangular flower bed. Side A is 15 feet long, side B is 3 feet longer than side A, and side C is 2 feet longer than side B. What is the total length of the fence Liam needs to buy?
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Correct answer: A — 53 feet
First, find the lengths of all three sides. Side $$A = 15$$ feet. Side $$B = 15 + 3 = 18$$ feet. Side $$C = 18 + 2 = 20$$ feet. The total length of the fence is the perimeter of the triangle: Total Length $$= 15 + 18 + 20 = 53$$ feet.
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Question 9 hard
Two interior angles of a triangle measure 45 degrees and 65 degrees. What is the measure of the third interior angle?
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Correct answer: B — 70 degrees
The sum of the interior angles in any triangle is always 180 degrees. Let x be the measure of the third angle: $$45 + 65 + x = 180 \Rightarrow 110 + x = 180 \Rightarrow x = 70$$ degrees.
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Question 10 hard
A hexagonal running track has six equal sides that are each 1,320 feet long. If Sarah runs around the entire track four times, what is the total distance she covers?
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Correct answer: C — 31,680 feet
The perimeter of the regular hexagonal track is the sum of its six equal sides: Perimeter = $$6 \times 1{,}320$$ feet = 7,920 feet. Running around the track four times means covering four times the perimeter: Total Distance $$= 7{,}920 \times 4 = 31{,}680$$ feet.
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Question 11 hard
A rectangular playground has a perimeter of 300 feet. If the sum of the lengths of the two shorter sides is 80 feet, what is the length of each of the two longer sides?
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Correct answer: A — 110 feet
The perimeter of a rectangle is the sum of all four sides: $$P = (\text{sum of two shorter sides}) + (\text{sum of two longer sides})$$. Given $$P = 300$$ feet and the sum of the two shorter sides is 80 feet: $$300 = 80 + (\text{sum of two longer sides}) \Rightarrow \text{sum of two longer sides} = 220$$ feet. Since both longer sides are equal, the length of each longer side is $$\frac{220}{2} = 110$$ feet.