Free Quantitative Reasoning MCQs with Answers

151. The sum of two numbers is 14 and the ratio of the two numbers is −3 . What is the product of the two numbers?

• A. -105
• B. -119
• C. -133
• D. -147

Explanation: Let's solve the problem step by step:First, let the two numbers be x and y. We are given:x + y = 14andx/y = -3From the ratio x/y = -3, we can express x as x = -3y.Substitute x = -3y into the sum equation:-3y + y = 14This simplifies to:-2y = 14Solving for y gives:y = -7Now, substitute y = -7 back into x = -3y:x = -3(-7) = 21The two numbers are 21 and -7. Their product is:21 × (-7) = -147Therefore, the answer is D) -147.Options A, B, and C are incorrect as they result from errors in the substitution or arithmetic process.

152. If 2(x-y)=3y, what is the ratio x/y?

• A. 2/5
• B. 4/3
• C. 5/2
• D. 8/3

Explanation: Start with the equation: 2(x-y) = 3y. Expand the left side to get 2x - 2y = 3y. Next, add 2y to both sides: 2x = 5y. Divide both sides by y to isolate x: x/y = 5/2. Thus, the correct ratio is 5/2, which corresponds to Option C.Other options are incorrect due to errors in algebraic manipulation or misinterpretation of the equation. Option A (2/5) and Option B (4/3) arise from incorrect steps in rearranging and solving. Option D (8/3) results from a miscalculation.

153. The ratio of length to width of a rectangular garden is 6:7 . If the perimeter of the rectangle is 78 meters, what is the area of the garden in square meters?

• A. 274
• B. 326
• C. 352
• D. 378

Explanation: The ratio of the length to the width of the garden is 6:7. Let the common factor be 'x', so the length is 6x and the width is 7x. The perimeter of the rectangle is given by the formula 2(length + width). Therefore:2(6x + 7x) = 26x = 78Solving for 'x' gives:x = 78 / 26 = 3Thus, the length is 6 * 3 = 18 meters and the width is 7 * 3 = 21 meters.The area of the garden is calculated as:Area = length * width = 18 * 21 = 378 square meters.Therefore, Option D, 378, is the correct answer. The other options are incorrect as they do not align with the correct calculations based on the given information.

154. If 20 machines produce 1,240 printers in a day, how many more machines are needed to produce 1,984 printers in a day?

• A. 12
• B. 20
• C. 24
• D. 32

Explanation: To determine how many more machines are needed, set up a proportion based on the given information. We know that 20 machines produce 1,240 printers in a day. To produce 1,984 printers, let x be the additional machines needed: 20 machines / 1,240 printers = (20 + x) machines / 1,984 printers Cross-multiply to solve for x: 20 * 1,984 = (20 + x) * 1,240 39,680 = 24,800 + 1,240x 14,880 = 1,240x x = 14,880 / 1,240 = 12 Therefore, 12 more machines are needed. Option A is correct. Options B, C, and D represent incorrect calculations or assumptions about the production increase required.

155. If ¾ quart of lemonade concentrate is mixed with 6 ⅔ quarts of water to make lemonade for 40 people, how many quarts of lemonade concentrate are needed to make the lemonade for 24 people?

• A. 3/10
• B. 7/20
• C. 2/5
• D. 9/20

Explanation: To solve this problem, we need to set up a proportion based on the original mixture for 40 people. We have ¾ quart of concentrate for 40 people. We want to find out how much concentrate is needed for 24 people.Set up the proportion: (¾ quart / 40 people) = (x quart / 24 people).By cross-multiplying, we get: 40x = 24 × ¾. Simplifying this gives x = 18/40 = 9/20.Therefore, 9/20 quarts of concentrate are needed for 24 people. This maintains the same ratio of concentrate to people as the original mixture.The other options are incorrect because they do not maintain the correct proportion based on the original recipe.

156. A 32-acre field yields 768 bushels of corn each year. How many more acres are needed to yield 960 bushels of corn each year?

• A. 6
• B. 8
• C. 10
• D. 12

Explanation: To determine the additional acres required, set up a proportion based on the initial data: a 32-acre field yields 768 bushels. Express this as a ratio: 32 acres/768 bushels = (32 + x) acres/960 bushels, where 'x' is the number of additional acres needed.Cross-multiply to obtain: 32 * 960 = (32 + x) * 768.Upon solving, you get 30,720 = 24,576 + 768x.Further simplification gives 6,144 = 768x, leading to x = 8.Therefore, 8 more acres are required to reach the desired yield of 960 bushels. Other options either underestimate or overestimate the necessary acres based on incorrect calculations of the proportion.

157. A tree is 8 feet tall and grows 8 inches each year. In how many years will the tree reach a height of 30 feet?

• A. 27
• B. 33
• C. 45
• D. 52

Explanation: The tree currently stands at 8 feet tall and needs to reach 30 feet, which means it must grow an additional 22 feet.The tree grows 8 inches per year. Since there are 12 inches in a foot, 8 inches equals 2/3 of a foot per year.To find the number of years required for the tree to grow those 22 feet, divide the total feet needed by the annual growth in feet:Number of years = 22 feet / (2/3 feet/year) = 33 years.Therefore, it will take 33 years for the tree to reach a height of 30 feet. Option B is correct. The other options result from errors in conversion or in calculating the growth period.

158. In a certain room the ratio of males to females is 4 to 5. After 8 males enter the room, the ratio of males to females is 6 to 5. What is the total number of people in the room before the additional males enter the room?

• A. 27
• B. 36
• C. 45
• D. 54

Explanation: To solve this problem, start by defining variables for the number of males and females in the room. Let the number of males be 4x and the number of females be 5x, based on the initial ratio of 4 to 5.The equation for the initial setup is: 4x / 5x = 4 / 5 (which holds true by definition)When 8 additional males enter, the number of males becomes 4x + 8. The new ratio of males to females is given as 6 to 5:(4x + 8) / 5x = 6 / 5Cross-multiply to solve for x: 5(4x + 8) = 6(5x) 20x + 40 = 30x 10x = 40 x = 4Substitute x back to find the number of males and females: Number of males = 4x = 16 Number of females = 5x = 20The total number of people initially in the room is 16 + 20 = 36. Thus, the correct answer is (B) 36.Options A, C, and D result from incorrect calculations or assumptions in setting up the problem or solving the equations.

159. A person is born every 5 seconds and a person dies every 12 seconds. How many seconds does it take for the population to grow by one person?

• A. 7 sec
• B. 8 4⁄7 sec
• C. 10.5 sec
• D. 10 5⁄7 sec

Explanation: Time it takes for the population to grow by one person = "x" seconds.In "x" seconds, the number of people born would be "x/5" and the number of people who died would be "x/12".So the net increase in the population would be:x/5 - x/12We want this net increase to be equal to 1, since we are interested in finding the time it takes for the population to grow by one person.Therefore, we can set up the equation:x/5 - x/12 = 1Multiplying both sides by the least common multiple of 5 and 12, which is 60, we get:12x - 5x = 60Simplifying:7x = 60x = 60/7 secondsWe can convert this into a mixed number to get:x = 8 4/7 secondsTherefore, the answer is (B) 8 4/7 seconds.

160. Which of the following is equivalent to 0.03 % of 4?

• A. 0.12
• B. 0.012
• C. 0.0012
• D. 0.00012

Explanation: To solve the problem, first understand that a percentage is a fraction of 100. Therefore, 0.03% can be written as the decimal 0.0003 by dividing by 100. To find 0.03% of 4, you multiply the decimal by the number: 0.0003 x 4 = 0.0012.Thus, the correct answer is 0.0012 (Option C). The other options are incorrect due to errors in converting the percentage to a decimal or mistakes in calculation.