Free Quantitative Reasoning MCQs with Answers

31. A container that can hold 12 litres is 3/4 full. How much will it contain after 4 litres has been poured out of it?

• A. 5 litres
• B. 6 litres
• C. 8 litres
• D. 12 litres

Explanation: A full container holds 12 litres. Being 3/4 full means it contains 9 litres (as 3/4 of 12 is 9). After pouring out 4 litres, subtracting 4 from 9 results in 5 litres remaining. Therefore, the correct answer is 5 litres. The other options do not accurately represent the remaining volume after pouring out the specified volume.

32. Find the value of x such that 8x-3= 164-x

• A. 4
• B. 11/3
• C. 7/2
• D. 25/7

Explanation: To solve 8x-3 = 164-x, express both numbers as powers of 2: 8 = 23 and 16 = 24. Thus, rewrite the equation as (23)x-3 = (24)4-x. This simplifies to 23(x-3) = 216-4x. Since the bases are the same, equate the exponents: 3(x-3) = 16-4x. Solving for x gives 3x - 9 = 16 - 4x, leading to 7x = 25, so x = 25/7.The other options (4, 11/3, and 7/2) do not satisfy this equation when substituted back, indicating errors in setting up or solving the equation.

33. If 3x= 27 and 22x= ?

• A. 32
• B. 64
• C. 8
• D. 9

Explanation: To solve the problem, first determine the value of x from the equation 3x = 27. Recognizing that 27 is 33, we equate the exponents to find x = 3. Next, substitute x into 22x to solve for 26. Calculating 26 gives 64. Therefore, the correct answer is 64. The other options, 32, 8, and 9, arise from incorrect calculations or assumptions about the exponent values.

34. The expression (6n - 5)(n+4) is equivalent to:

• A. 6n2-20
• B. 6n2-19n - 20
• C. 6n2 - 29n - 20
• D. 6n2+ 19n - 20

Explanation: Apply Multiplicative Distribution Law: 6n(n+4)-5(n+4) Apply Multiplicative Distribution Law: 6nxn+6n×4-5n-5×4 Multiply the monomials: 6n²+24n-5n-5×4 Calculate the product or quotient: 6n2+24n-5n-20 Reorder and gather like terms: 6n2+(24n-5n)-20 Collect coefficients for the like terms: 6n2+(24-5)×n-20 Calculate the sum or difference: 6n2+19n-20 Check equivalency: True Answer: True

35. (6a - 12) - (4a + 4) = ?

• A. 2(a+2)
• B. 2(a + 4)
• C. 2(a-2)
• D. 2(a-8)

Explanation: To solve this problem, combine like terms, keeping track of the negatives. The expression (6a - 12) - (4a + 4) becomes 6a -12 - 4a - 4, which can be simplified to 2a - 16. The coefficient 2 can be factored out of both terms to get 2(a - 8).

36. The average of 25 and _ is 2013

• A. 994
• B. 1019
• C. 1988
• D. 4001

Explanation: Let the missing number be x (25 + x)/2 = 2013 25+x= 2013 × 2 25+ x= 4026 x=4026-25 x= 4001

37. Point A is to be graphed in a quadrant, not on an axis, of the standard (x, y) coordinate plane below. If the x-coordinate and the y-coordinate of point A are to have the same signs, then point A must be located in

• A. Quadrant I only
• B. Quadrant II only
• C. Quadrant III only
• D. Quadrant I or II only
• E. Quadrant I or III only

Explanation: Option E is correct since both quadrant I and III has x-axis and y-axis with similar signs.

38. 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. -1/2ma = mb
• D. ma-1=mb
• E. ma - mb = 0

Explanation: The correct answer is a. Perpendicular lines intersect to form right angles, and their slopes are negative reciprocals of each other. In this case, if the slope of line a is ma, the slope of line b is -1/ma. Since the slope of line b is mb, we have mb = -1/ma, which simplifies to ma = -1/mb. The other options do not reflect the relationship between slopes of perpendicular lines, making them incorrect.

39. In the standard (x,y) coordinate plane, which of the following lines goes through (3,4) and is parallel to y=2x+2?

• A. y = 1/2x + 2
• B. y=2x-2
• C. y = 2x + 4
• D. y = 2x + 10
• E. y = 3x + 2

Explanation: Parallel lines have the same slope, so a line parallel to y = 2x + 2 should also have a slope of 2. Option B, y = 2x - 2, meets this criteria and passes through the point (3,4), making it the correct answer. Other options either have incorrect slopes or do not pass through the specified point.

40. What is the slope of any line parallel to the line 2x - 3y = 7?

• A. -3
• B. -⅔
• C. ⅔
• D. 2

Explanation: To find the slope of any line parallel to 2x - 3y = 7, rearrange the equation to y = mx + b. By solving for 'y', -3y = -2x + 7 becomes y = (2/3)x - 7/3. The slope 'm' is 2/3. Since parallel lines have the same slope, the correct answer is ⅔. Options -3, -⅔, and 2 are incorrect as they did not correctly determine the slope or misunderstood the process of finding it from the equation.