Free Quantitative Reasoning MCQs with Answers

431. 43, 83, 54, 35, 77, x, y If the median of the set of numbers is 54 and the mean is 56, which of the following could be the values of x and y?

• A. 41 and 59
• B. 65 and 72
• C. 56 and 80
• D. 21 and 52

Explanation: Known numbers in ascending order are; 35, 43, 54, 77, 83 For 54 to remain median, one of the x and y should be greater and other less than 54, as satisfied by option A. Further, we need to confirm if the mean is 56, if x= 41 and y= 59. 35, 41, 43, 54, 59, 77, 83 (35+41+43+54+59+77+83)/7 = 392/7=56

432. Given the graph below in the standard (x,y) coordinate plane, the slope of line a is ma and the slope of line b is mb. Which of the following statements about the slope of lines a and b is true?

• A. ma= - 1/ mb
• B. ma+mb=0
• C. -I/2ma = mb
• D. ma-1=mb
• E. ma - mb = 0

Explanation: The correct answer is a. Based on the figure, line a and line b are perpendicular lines, because they intersect to form right angles. Perpendicular lines have slopes that are negative reciprocals. In other words, if the slope of line a is ma , the slope of line b is −1/mα. You are given that the slope of line b is mb , so mb = −1/mα. This is equivalent to mα = −1/mb

433. What is the slope-intercept form of 6x - 2y - 4 = 0?

• A. y=6x-2
• B. y = 3x + 2
• C. y = 3x-2
• D. y = −6x - 4

Explanation: The correct answer is C. The slope-intercept form of the equation of a line states that y=m x+b. To find the slope-intercept form of the equation 6x-2y-4=0, you must isolate y on the left side of the equation as follows: 6x-2y-4=0 -2y=-6x+4 th -2y-4--6x y=3x-2 If you selected answer choice D, you probably forgot to switch the signs when dividing by 2. It is crucial to multiply all terms on both sides of the equation to arrive at a correct answer.

434. For a certain quadratic equation, ax2 + bx + c = 0, the 2 solutions are x = ¾ and x =-⅖ . Which of the following could be factors of ax2 + bx + c?

• A. (4x-3) AND (5x+2)
• B. (4x2) AND (5x+3)
• C. (4x+2) AND (5x-3)
• D. (4x+3) AND (5x-2)
• E. (4x+3) AND (5x+2)

Explanation: For a certain quadratic equation ax2 + bx + c = 0, if x = a/b is a solution, then a possible factor would be (bx − a). Since two solutions for ax2 + bx + c = 0 are x = 3/4 and x = -2/5, then possible factors are (4x − 3) and (5x + 2).

435. |2x+1|=5 If a and b are the solutions to the equation above, wat 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.

436. 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 ≤ 20
• B. s ≤ 150
• C. s ≤ 170
• D. 150 ≤ s ≤ 170

Explanation: Choice D is correct. It's given that during a portion of a flight, a small airplane's cruising speed varies between 150 miles per hour and 170 miles per hour. It's also given that s represents the cruising speed, in miles per hour, during this portion of the flight. It follows that the airplane's cruising speed, in miles per hour, was at least 150, which means s ≥150, and was at most 170, which means s ≤ 170. Therefore, the inequality that best represents this situation is 150 ≤ s ≤ 170.

437. 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 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. The slope of the line of best fit is negative, meaning as the distance of planetoids from the Sun increases, the density of the planetoids decreases. Therefore, planetoids that are more distant from the Sun tend to have lesser densities.

438. 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.If Mosteller's and Current's formulas give the same estimate for A, which of the following expressions is equivalent to √hw?

• A. 4 + w / 2
• B. 4 + w / 1,800
• C. 2(4 + w)
• D. (4 + w)2 / 2

Explanation: Choice C is correct. If Mosteller's and Current's formulas give the same estimate for A, then the right-hand sides of these two equations are equal; that is, √hw / 60 = 4 + w / 30. Multiplying each side of this equation by 60 to isolate the expression √hw gives √hw = 60 (4+w/30) or √hw = 2(4+w). Therefore, if Mosteller's and Current's formulas give the same estimate for A, then √hw is equivalent to 2(4 + w). An alternate approach is to multiply the numerator and denominator of Current's formula by 2, which gives 2(4+w) / /60. Since it is given that Mosteller's and Current's formulas give the same estimate for A, 2(4+w) / 60 = √hw/60.Therefore, √hw = 2(4 + w).

439. A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 cm2, and the height of the can is 10 cm. If 110 cm3 of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?

• A. 7.5 cm3
• B. 185 cm3
• C. 640 cm3
• D. 750 cm3

Explanation: Choice C is correct. The total volume of the cylindrical can is found by multiplying the area of the base of the can, 75 cm2, by the height of the can, 10 cm, which yields 750 cm3. If the syrup needed to fill the can has a volume of 110 cm3, then the remaining volume for the pieces of fruit is 750 - 110 = 640 cm3.

440. Beginning in the 1950s, Navajo Nation legislator Annie Dodge Wauneka continuously worked to promote public health; this _ effort involved traveling throughout the vast Navajo homeland and writing a medical dictionary for speakers of Diné bizaad, the Navajo language. Which choice completes the text with the most logical and precise word or phrase

• A. impartial
• B. Offhand
• C. persistent
• D. mandatory

Explanation: Choice C is the best answer because it most logically completes the text's discussion of Annie Dodge Wauneka's work as a Navajo Nation legislator. As used in this context, "persistent" means existing continuously. The text states that Wauneka "continuously worked to promote public health," traveling extensively and authoring a medical dictionary; this indicates that Wauneka's effort was persistent.