Free Quantitative Reasoning MCQs with Answers

211. |14| * |-2|=?

• A. -28
• B. -16
• C. -12
• D. 16
• E. 28

Explanation: Matrices can be multiplied, the correct method gives the answer as such. You can only multiply two matrices if their dimensions are compatible , which means the number of columns in the first matrix is the same as the number of rows in the second matrix. If A=[aij] is an m×n matrix and B=[bij] is an n×p matrix, the product AB is an m×p matrix. AB=[cij] , where cij=ai1b1j+ai2b2j

212. If |x-3| > 10, which of the following could be the value of |x|?

• A. 2
• B. 4
• C. 6
• D. 8

Explanation: Test each of the answer choices, making sure to include the negative possibilities. For example, the answer is not (A) because when x=2 or −2,∣x−3∣ is not greater than 10 . However, ∣x−3∣ is greater than 10 when x=−8.

213. In the xy-plane, the graph of the function f(x) = x2 + 5x + 4 has two x-intercepts. What is the distance between the x-intercepts?

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Explanation: To find the distance between these two points, we can use the distance formula: d = |x₂ - x₁| where x₁ = -1 and x₂ = -4. Substituting the values, we get: d = |-4 - (-1)| = |-4 + 1| = 3 Therefore, the distance between the x-intercepts is 3. Hence, the correct option is (C) 3.

214. Which of the following statements is true about the graph of the equation 2y - 3x = -4 in the xy-plane?

• A. It has a negative slope and a positive y-intercept.
• B. It has a negative slope and a negative y-intercept.
• C. It has a positive slope and a positive y-intercept.
• D. It has a positive slope and a negative y-intercept.

Explanation: The graph of the equation 2y - 3x = -4 has a positive slope and a negative y-intercept.

215. |2x+1|=5If a and b are the solutions to the equation above, what is the value of |a-b|?

• A. -5
• B. 1
• C. 5
• D. -1

Explanation: Now, to find the value of |a-b|, we can use the absolute value of the difference between a and b. In this case, a=2 and b=-3, so |a-b| = |2-(-3)| = |2+3| = 5. Therefore, the value of |a-b| is 5, as mentioned.

216. The scatterplot shows the relationship between two variables, x and y. Which of the following graphs shows the most appropriate model for the data?

• A. A
• B. B
• C. C
• D. D

Explanation: Choice D is correct because it provides a model in the form of an increasing curve that closely follows the trend of the data points in the scatterplot. The data points exhibit an increasing, non-linear trend, and the model in option D accurately captures this trend with points both above and below the curve. Option A is incorrect because it suggests a linear model, which does not fit the curved trend. Option B is incorrect due to its decreasing line, which contradicts the increasing trend of the data points. Option C is incorrect because its model is positioned above all data points, failing to represent the data accurately.

217. During a portion of a flight, a small airplane's cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where s is the cruising speed, in miles per hour, during this portion of the flight?

• A. s < 150 or s > 170
• B. s < 150
• C. s > 170
• D. 150 ≤ s ≤ 170

Explanation: The correct answer is 150 ≤ s ≤ 170. This inequality accurately represents the range of the cruising speed as described in the problem. The speed is not less than 150 miles per hour and not greater than 170 miles per hour, so both endpoints must be included. Other options incorrectly suggest speeds outside this range or do not represent the situation described in the problem.

218. y > 4x + 8For which of the following tables are all the values of x and their corresponding values of y solutions to the given inequality?

• A. A
• B. B
• C. C
• D. D

Explanation: Choice A is correct. In each choice, the values of x are 2, 4, and 6. Substituting the first value of x, 2, for x in the given inequality yields y > 4(2) + 8, or y > 16. Therefore, when x=2, the corresponding value of y must be greater than 16. Of the given choices, only choice A is a table where the value of y corresponding to x=2 is greater than 16. To confirm that the other values of x in this table and their corresponding values of y are also solutions to the given inequality, the values of x and y in the table can be substituted for x and y in the given inequality. Substituting 4 for x and 30 for y in the given inequality yields 30 > 4(4) + 8, or 30 > 24. which is true. Substituting 6 for x and 41 for y in the given inequality yields 41 > 4(6) + 8, or 41 > 32. , which is true. It follows that for choice A, all the values of x and their corresponding values of y are solutions to the given inequality.

219. Which expression is equivalent to (x2 + 11)2 + (x - 5)(x + 5)?

• A. x4 + 23x2 - 14
• B. x4 + 23x2 + 96
• C. x4 + 12x2 +121
• D. x4 + x2 + 146

Explanation: Choice B is correct. The expression (x2 + 11)2 can be written as (x2 + 11)(x2 + 11), which is equivalent to x2(x2 + 11) + 11(x2 + 11). Distributing x2 and 11 to (x2 + 11) yields x4 + 11x2 + 11x2 + 121, or x4 + 22x2 + 121.The expression (x - 5)(x + 5) is equivalent to (x-5)x + (x-5)5. Distributing x and 5 to (x-5) yields x2 - 5x + 5x - 25, or x2 - 25. Therefore, the expression (x2 + 11)2 + (x - 5)(x + 5) is equivalent to (x4 + 22x2 + 121) + (x2 - 25), or x4 + 22x2 + 121 + x2 - 25.Combining like terms in this expression yields x4 + 23x2 + 96.

220. The relationship between two variables, x and y, is linear. For every increase in the value of x by 1, the value of y increases by 8. When the value of x is 2, the value of y is 18. Which equation represents this relationship?

• A. y = 2x + 18
• B. y = 2x + 8
• C. y = 8x + 2
• D. y = 3x + 26

Explanation: Choice C is correct. It's given that the relationship between x and y is linear. An equation representing a linear relationship can be written in the form y = mx + b, where m is the slope and b is the y-coordinate of the y-intercept of the graph of the relationship in the xy-plane. It's given that for every increase in the value of x by 1, the value of y increases by 8. The slope of a line can be expressed as the change in y over the change in x. Thus, the slope, m, of the line representing this relationship can be expressed as 8/1, or 8. Substituting 8 for m in the equation y = mx + b yields y = 8x + b. It's also given that when the value of x is 2, the value of y is 18. Substituting 2 for x and 18 for y in the equation y = 8x + b yields 18 = 8(2) + b, or 18= 16 + b. Subtracting 16 from each side of this equation yields 2=b. Substituting 2 for b in the equation y = 8x + b yields y = 8x + 2. Therefore, the equation y = 8x + 2 represents this relationship.