Arithmetic Reasoning Practice Test 8

Correct answer: A — 14 centimeters

The radius of a circle is half of its diameter. Therefore, the radius is $$\frac{28}{2} = 14$$ centimeters.

Correct answer: B — 35 meters

The formula for the perimeter of a rectangle is $$P = 2(\text{length} + \text{width})$$. Given $$P = 120$$ and width = 25, we have $$120 = 2(\text{length} + 25) \Rightarrow 60 = \text{length} + 25 \Rightarrow \text{length} = 60 - 25 = 35$$ meters.

Correct answer: B — $240.00

A square has 4 equal sides, so its perimeter is $$4 \times 15 = 60$$ feet. The total cost is the perimeter multiplied by the cost per foot: 60 × $4.00 = $240.00.

Correct answer: B — 180 square feet

The area of a rectangle is calculated by multiplying its width by its length. Area = 12 feet × 15 feet = 180 square feet.

Correct answer: A — $102.00

First, find the area of the room in square feet: 9 feet × 12 feet = 108 square feet. Convert the area to square yards: $$\frac{108}{9} = 12$$ square yards. Finally, multiply by the cost per square yard: 12 × $8.50 = $102.00.

Correct answer: A — 20 meters

Let the width be w. The length is $$3w - 10$$. The perimeter is $$2(\text{length} + \text{width}) = 2((3w - 10) + w) = 2(4w - 10) = 8w - 20$$. Given the perimeter is 140 meters: $$8w - 20 = 140 \Rightarrow 8w = 160 \Rightarrow w = 20$$ meters.

Correct answer: A — 25 meters

Let the width be w. The length is $$2w + 15$$. The perimeter is $$2(\text{length} + \text{width}) = 2((2w + 15) + w) = 2(3w + 15) = 6w + 30$$. Given the perimeter is 180 meters: $$6w + 30 = 180 \Rightarrow 6w = 150 \Rightarrow w = 25$$ meters.

Correct answer: B — 24 boxes

The planter box is a square prism with a length of 4 feet, width of 4 feet, and height of 1.5 feet. Volume = length × width × height = $$4 \times 4 \times 1.5 = 24$$ cubic feet. Since each box contains 1 cubic foot, $$\frac{24}{1} = 24$$ boxes are required.

Correct answer: A — 100 feet × 160 feet

Let the original width be w. The original length is $$w + 60$$. If the width is reduced by 20, the new width is $$w - 20$$. The length $$(w + 60)$$ becomes double the new width: $$w + 60 = 2(w - 20) \Rightarrow w + 60 = 2w - 40 \Rightarrow w = 100$$ feet (original width). The original length is $$100 + 60 = 160$$ feet.

Correct answer: B — $412.50

First, calculate the total area of the backyard. The rectangle area = 10 yd × 6 yd = 60 sq yd. The triangle area = 0.5 × base × height = $$0.5 \times 10$$ yd × 3 yd = 15 sq yd. Total area $$= 60 + 15 = 75$$ sq yd. Cost of turf = 75 × $4.50 = $337.50. Cost of labor = 5 hours × $15/hour = $75. Total cost = $337.50 + $75 = $412.50.

Correct answer: A — 27,000

First, find the revolutions per second: 4,500 revolutions / 60 seconds = 75 revolutions per second. Since one full revolution is 360 degrees, the total rotation in one second is: $$75 \times 360 = 27{,}000$$ degrees.

Correct answer: A — 750 square meters

Let the width be w. The length is $$3w + 5$$. Perimeter $$= 2(\text{length} + \text{width}) = 2((3w + 5) + w) = 2(4w + 5) = 8w + 10$$. Given perimeter is 130: $$8w + 10 = 130 \Rightarrow 8w = 120 \Rightarrow w = 15$$ meters. The length is $$3(15) + 5 = 50$$ meters. The area of the garden is width × length $$= 15 \times 50 = 750$$ square meters.