Free Quantitative Reasoning MCQs with Answers

351. A fish swam a distance of 5,104 yards. How far did the fish swim, in miles? (1 mile = 1,760 yards)

• A. 0.2
• B. 2.9
• C. 3.344
• D. 6.864

Explanation: Choice B is correct. To convert yards to miles, use the conversion factor: 1 mile = 1,760 yards. Divide 5,104 yards by 1,760 yards/mile to convert the distance from yards to miles, resulting in approximately 2.9 miles. Option A significantly underestimates the distance, while Options C and D overestimate it due to calculation errors.

352. f(x ) = 7x +1The function gives the total number of people on a company retreat with x managers. What is the total number of people on a company retreat with 7 managers?

• A. 50.
• B. (16, 2)
• C. (17, 1)
• D. (18, 0)

Explanation: The correct answer is 50. It's given that the function f gives the total number of people on a company retreat with x managers. It's also given that 7 manager sare on the company retreat. Substituting 7 for x in the given function yields f(7 ) (771 ) (750 ) 7 50 = . Therefore, there are a total of 50 people on a company retreat with 7 managers.

353. h (x ) = 2x −3Which table gives three values of x and their corresponding values of h (x ) for the given function h?

• A. xh(x)1-22134
• B. xh(x)1-12133
• C. xh(x)1-12335
• D. xh(x)102234

Explanation: To determine the correct table, substitute each value of x into the function h(x) = 2x - 3. For x = 1, h(x) = 2(1) - 3 = -1. For x = 2, h(x) = 2(2) - 3 = 1. For x = 3, h(x) = 2(3) - 3 = 3. Therefore, the correct table is Choice B. The other options do not correctly apply the function to the given values of x, resulting in incorrect corresponding h(x) values.

354. A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600 pounds. What is the maximum number of boxes this truck can tow in a trailer with am weight of 500 pounds if each box weighs 120 pounds?

• A. 34
• B. 35
• C. 38
• D. 39

Explanation: Choice A is correct. It's given that the truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600 pounds. If the trailer has a weight of 500 pounds and each box weighs 120 pounds, the expression 500 + 120b, where b is the number of boxes, gives the combined weight of the trailer and the boxes. Since the combined weight must be no more than 4,600 pounds, the possible numbers of boxes the truck can tow are given by the inequality 500 + 120b ≤ 4,600 . Subtracting 500 from both sides of this inequality yields 120b ≤ 4,100 . Dividing both sides of this inequality by 120 yields b ≤ 205/6 , or b is less than or equal to approximately 34.17. Since the number of boxes, b, must be a whole number, the maximum number of boxes the truck can tow is the greatest whole number less than 34.17, which is 34.

355. The regular price of a shirt at a store is $11.70. The sale price of the shirt is 80% less than the regular price, and the sale price is 30% greater than the store's cost for the shirt. What was the store's cost, in dollars, for the shirt?

• A. 1.8
• B. 1.9
• C. 1.6
• D. 1.5

Explanation: The correct answer is 1.8. It's given that the regular price of a shirt at a store is $11.70, and the sale price of the shirt is 80% less than the regular price. It follows that the sale price of the shirt is $11.70 (1- 80/100), or $11.70 (1 - 0.8), which is equivalent to $2.34. It's also given that the sale price of the shirt is 30%greater than the store's cost for the shirt. Let x represent the store's cost for the shirt. It follows that 2.34 = (1+30/100)x, or 2.34 = 1.3x. Dividing both sides of this equation by 1.3 yields x =1.80. Therefore, the store's cost, in dollars, for the shirt is 1.80. Note that 1.8 and 9/5 are examples of ways to enter a correct answer.

356. What is the y-intercept of the graph shown?

• A. (0, 0)
• B. (0, 2)
• C. (2, 0)
• D. (2, 2)

Explanation: The y-intercept is the point where the graph intersects the y-axis. This occurs when the x-coordinate is 0. In this graph, the y-intercept is correctly identified as (0, 2), as this is where the graph crosses the y-axis. Options A, C, and D are incorrect as they do not represent the point at which the graph crosses the y-axis. Option A (0, 0) is the origin, which is not applicable here. Option C (2, 0) represents an x-intercept, and option D (2, 2) is a point on the graph but not on the y-axis.

357. What length, in centimeters, is equivalent to a length of 51 meters? (1 meter = 100 centimeters)

• A. 0.051
• B. 0.51
• C. 5,100
• D. 51,000

Explanation: The correct answer is 5,100 centimeters. To convert meters to centimeters, you multiply the number of meters by 100 because there are 100 centimeters in a meter. Thus, 51 meters equals 5,100 centimeters. Options A and B incorrectly involve dividing by 100 instead of multiplying. Option D is the conversion of meters to millimeters, as there are 1,000 millimeters in a meter, not the required centimeters.

358. A circle has center O, and points R and S lie on the circle. In triangle ORS, the measure of ∠ROS is 88°. What is the measure of ∠RSO, in degrees?

• A. 45
• B. 46
• C. 48
• D. 56

Explanation: The correct answer is 46. It's given that O is the center of a circle and that points R and S lie on the circle. Therefore, OR and OS are radii of the circle. It follows that OR = OS. If two sides of a triangle are congruent, then the angles opposite them are congruent. It follows that the angles ∠ RSO and ∠ORS, which are across from the sides of equal length, are congruent. Let x° represent the measure of ∠ RSO. It follows that the measure of ∠ORS is also x°. It's given that the measure of ∠ ROS is 88°. Because the sum of the measures of the interior angles of a triangle is 180°, the equation x° + x° + 80°= 180° or 2x + 88 = 180, can be used to find the measure of ∠ RSO. Subtracting 88 from both sides of this equation yields 2x = 92. Dividing both sides of this equation by 2 yields x = 46. Therefore, the measure of ∠ RSO, in degrees, is 46.

359. The minimum value of x is 12 less than 6 times another number n. Which inequality shows the possible values of x ?

• A. x ≤ 6n − 12
• B. x ≥ 6n − 12
• C. x ≤ 12 − 6n
• D. x ≥ 12 − 6n

Explanation: The correct answer is Choice B: x ≥ 6n − 12. The problem states that the minimum value of x is 12 less than 6 times another number n. Translating this into an inequality, we get x must be greater than or equal to (6n - 12). Choices A and C are incorrect because they reverse the role of the minimum and maximum values. Choice D is incorrect because it incorrectly positions the number 12 and the term 6n in the inequality, suggesting a different relationship than what is stated in the problem.

360. A proposal for a new library was included on an election ballot. A radio show stated that 3 times as many people voted in favor of the proposal as people who voted against it. A social media post reported that 15,000 more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?

• A. 7,500
• B. 15,000
• C. 22,500
• D. 45,000

Explanation: To solve the problem, let x be the number of people who voted against the proposal. According to the radio show, 3 times as many people voted in favor, which translates to 3x. The social media post states there were 15,000 more votes in favor, so 3x - x = 15,000. Simplifying gives 2x = 15,000, so x = 7,500. Thus, 7,500 people voted against the proposal. Option B is incorrect because it describes the extra number of people who voted in favor, not those who voted against. Option C is incorrect as it represents the total number of people who voted in favor. Option D is a calculation error, as no group of voters matches this number.