Arithmetic Reasoning Practice Test 7

Correct answer: B — 20,000 feet

The perimeter of a square park is 4 times the side length: $$4 \times 1{,}250 = 5{,}000$$ feet. Making four complete laps means multiplying the perimeter by 4: $$5{,}000 \times 4 = 20{,}000$$ feet.

Correct answer: A — 12 inches

The total ratio parts are $$4 + 1 = 5$$ parts. Each part represents $$\frac{60}{5} = 12$$ inches. The shortest piece corresponds to 1 part, which is $$1 \times 12 = 12$$ inches.

Correct answer: C — 88 cubic inches

The volume of a cylinder is $$V = \pi \times r^2 \times h$$. Using $$\pi = \frac{22}{7}$$, $$V = (\frac{22}{7}) \times (2^2) \times 7 = 22 \times 4 = 88$$ cubic inches.

Correct answer: A — 25 feet

The walkway forms the hypotenuse of a right triangle where the legs are 7 feet and 24 feet. By the Pythagorean theorem: $$c = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25$$ feet.

Correct answer: B — 66 meters

The distance around the edge is the circumference of the circle: $$C = \pi \times d$$. Using $$\pi = \frac{22}{7}$$ and a diameter of 21 meters: $$C = (\frac{22}{7}) \times 21 = 22 \times 3 = 66$$ meters.

Correct answer: B — 12 inches

Let D be the diameter of the sleeve. The diameter of the pipe is $$(\frac{3}{4}) \times D$$. The radius of the sleeve is $$\frac{D}{2}$$. According to the problem: $$\frac{D}{2} = (\frac{3}{4}) \times D - 3$$. Multiplying both sides by 4 gives: $$2 \times D = 3 \times D - 12$$. Solving for D, we get $$D = 12$$ inches.

Correct answer: B — 430 feet

The border needs to be installed along all complete wall sections. This includes the two long walls (150 feet each), one full short wall (80 feet), and the two partial wall sections on the other short wall (25 feet each). Total length = $$150 + 150 + 80 + 25 + 25 = 430$$ feet.

Correct answer: A — $315.00

First, find the area of the room in square feet: Area = $$12 \times 15 = 180$$ square feet. Convert this area to square yards by dividing by 9 (since 1 square yard = 9 square feet): $$\frac{180}{9} = 20$$ square yards. Calculate total cost: 20 × $15.75 = $315.00.

Correct answer: B — 62 square yards

The surface area of a rectangular prism is found using the formula: SA = $$2 \times (l \times w + w \times h + h \times l)$$. For a box with $$l = 5$$, $$w = 3$$, and $$h = 2$$: SA $$= 2 \times (5 \times 3 + 3 \times 2 + 2 \times 5) = 2 \times (15 + 6 + 10) = 2 \times (31) = 62$$ square yards.

Correct answer: B — 30 inches × 20 inches

Let l be the length. The width is $$(\frac{2}{3}) \times l$$. Area = length × width $$= l \times (\frac{2}{3}) \times l = (\frac{2}{3}) \times l^2$$. Given Area = 600: $$(\frac{2}{3}) \times l^2 = 600 \Rightarrow l^2 = 900 \Rightarrow l = 30$$ inches. The width is $$(\frac{2}{3}) \times 30 = 20$$ inches. Thus, the dimensions are 30 inches × 20 inches.

Correct answer: B — 37.70 feet

The formula for the circumference of a circle is $$C = 2 \times \pi \times r$$. With $$r = 6$$ feet: $$C = 2 \times \pi \times 6 = 12\pi \approx 37.70$$ feet.