Free Quantitative Reasoning MCQs with Answers

241. Which of the following ordered pairs (x, y) satisfies the inequality 5x −3y < 4?I. (1, 1)II. (2, 5)III. (3, 2)

• A. I only
• B. II only
• C. I and II only
• D. I and III only

Explanation: Option C is correct because both ordered pairs (1, 1) and (2, 5) satisfy the inequality 5x − 3y < 4. For (1, 1), substituting gives 2 < 4, which is true. For (2, 5), substituting gives −5 < 4, also true. However, substituting (3, 2) gives 9 < 4, which is false. Thus, (1, 1) and (2, 5) are the only ordered pairs that make the inequality true. Options A and B each miss one of the pairs that satisfy the inequality, and option D includes (3, 2), which does not satisfy the inequality.

242. In the equation (ax + 3)2 = 36, a is a constant. If x = −3 is one solution to the equation, what is a possible value of a?

• A. -11
• B. -5
• C. -1
• D. 0

Explanation: To solve the equation (ax + 3)2 = 36 with x = −3 as a solution, substitute −3 for x to get (−3a + 3)2 = 36. Taking the square root of both sides yields two possible equations: −3a + 3 = 6 and −3a + 3 = −6. Solving these, we find a = −1 and a = 3. Thus, −1 is a possible value for a. The incorrect options stem from common errors such as ignoring the squared term, incorrect arithmetic operations, or misinterpretation of the equation structure.

243. The scatterplot shows the densities of 7 planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown.According to the scatterplot, which of the following statements is true about the relationship between a planetoid's average distance from the Sun and its density?

• A. Planetoids that are more distant from the Sun tend to have lesser densities.
• B. Planetoids that are more distant from the Sun tend to have greater densities.
• C. The density of a planetoid that is twice as far from the Sun as another planetoid is exactly half the density of that other planetoid.
• D. The distance from a planetoid to the Sun is unrelated to its density.

Explanation: Choice A is correct because the scatterplot's line of best fit has a negative slope, indicating a negative correlation between the planetoids' average distance from the Sun and their densities. This means that as the distance increases, the density decreases. Option B is incorrect because it contradicts the negative trend shown in the scatterplot. Option C is incorrect because the relationship between distance and density is not a direct halving as suggested. Option D is incorrect because the presence of a line of best fit indicates that there is indeed a relationship between the two variables.

244. A software company is selling a new game in a standard edition and a collector's edition. The box for the standard edition has a volume of 20 cubic inches, and the box for the collector's edition has a volume of 30 cubic inches. The company receives an order for 75 copies of the game, and the total volume of the order to be shipped is 1,870 cubic inches. Which of the following systems of equations can be used to determine the number of standard edition games, s, and collector's edition games, c, that were ordered?

• A. 75 - s = c20s + 30c = 1,870
• B. 75 - s = c30s + 20c = 1,870
• C. s - c = 7525(s + c) = 1,870
• D. s - c = 7530s + 20c = 1,870

Explanation: Choice A is correct because it correctly sets up the system of equations based on the information provided. The equation 75 − s = c represents the total number of games ordered, and the equation 20s + 30c = 1,870 represents the total volume of the order. The other options either incorrectly swap the volumes for standard and collector's editions or make assumptions that do not align with the given scenario.

245. Theresa ran on a treadmill for thirty minutes, and her time and speed are shown on the graph above. According to the graph, which of the following statements is NOT true concerning Theresa's run?

• A. Theresa ran at a constant speed for five minutes.
• B. Theresa's speed was increasing for a longer period of time than it was decreasing.
• C. Theresa's speed decreased at a constant rate during the last five minutes.
• D. Theresa's speed reached its maximum during the last ten minutes.

Explanation: Choice B is correct. Theresa's speed was increasing from 0 to 5 minutes and from 20 to 25 minutes, which is a total of 10 minutes. Theresa's speed was decreasing from 10 minutes to 20 minutes and from 25 to 30 minutes, which is a total of 15 minutes. Therefore, Theresa's speed was NOT increasing for a longer period of time than it was decreasing.

246. In the figure, what is the value of x?

• A. 45
• B. 90
• C. 100
• D. 105

Explanation: Choice D is correct. A quadrilateral's interior angles sum up to 360°. To find x, set up the equation 45 + 3x = 360. First, subtract 45 from both sides to get 3x = 315. Then, divide by 3 to solve for x, resulting in x = 105. This value ensures the angles add up correctly to 360°. Other options do not satisfy this requirement as their calculated sums are less than 360°.

247. The formulas are used in medicine to estimate the body surface area A, in square meters, of infants and children whose weight w ranges between 3 and 30 kilograms and whose height h is measured in centimeters.Based on Current's formula, what is w in terms of A ?

• A. w = 30A − 4
• B. w = 30A + 4
• C. w = 30(A − 4)
• D. w = 30(A + 4)

Explanation: To solve for w in terms of A, start with the given formula A = 4 + w / 30. Multiply both sides by 30 to eliminate the fraction, resulting in 30A = 4 + w. Then, subtract 4 from both sides to isolate w, yielding w = 30A − 4. Option A is correct because it follows these steps correctly. Options B, C, and D each involve incorrect operations or rearrangements that do not accurately reflect the process of isolating w.

248. h(t) = −16t2 + 110t + 72The function above models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?

• A. The initial height, in feet, of the object
• B. The maximum height, in feet, of the object
• C. The initial speed, in feet per second, of the object
• D. The maximum speed, in feet per second, of the object

Explanation: Choice A is correct. The variable t represents the seconds after the object is launched. Since h(0) = 72, this, means that the height, in feet, at 0 seconds, or the initial height, is 72 feet.

249. The table gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food.If x food calories are equivalent to k kilojoules, of the following, which best represents the relationship between x and k?

• A. k = 0.24x
• B. k = 4.2x
• C. x = 4.2k
• D. xk = 4.2

Explanation: Choice B is correct because the relationship between x food calories and k kilojoules is best described by a proportional relationship. By considering the data points (4.0, 16.7) and (9.0, 37.7) from the table, we calculate the rate of change as (37.7 - 16.7) / (9.0 - 4.0) = 21/5 = 4.2, leading to the equation k = 4.2x. Other options are incorrect due to errors in setting up the relationship or reversing variables.

250. The table gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food.If the 180 food calories in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydrate, which of the following expresses f in terms of p and c?

• A. f = 20 + 4/9 (p + c)
• B. f = 20 - 4/9 (p + c)
• C. f = 20 - 4/9 (p - c)
• D. f = 20 + 9/4 (p + c)

Explanation: Choice B is correct. It is given that there are 4.0 food calories per gram of protein, 9.0 food calories per gram of fat, and 4.0 food calories per gram of carbohydrate. If 180 food calories in a granola bar came from p grams of protein, f grams of fat, and c grams of carbohydrate, then the situation can be represented by the equation 180 = 4p + 9f + 4c. The equation can then be rewritten in terms of f by subtracting 4p and 4c from both sides of the equation and then dividing both sides of the equation by 9. The result is the equation f = 20 - 4/9 (p + c).