Free Quantitative Reasoning MCQs with Answers

101. The cost of two dozen apples is $3.60. At this rate, what is the cost of 10 apples?

• A. $1.75
• B. $1.60
• C. $1.55
• D. $1.50

Explanation: To find the cost of 10 apples, begin by determining the cost of one apple. Since 24 apples cost $3.60, divide $3.60 by 24 to find the cost per apple: $3.60 ÷ 24 = $0.15 per apple.Now, multiply the cost per apple by the number of apples you want to buy: $0.15 × 10 = $1.50. So, the cost of 10 apples is $1.50.Option A ($1.75), Option B ($1.60), and Option C ($1.55) all overestimate the cost per apple or involve calculation errors, leading to incorrect total costs for 10 apples.To find the cost of 10 apples, let's break it down:Two dozen apples = 24 applesCost of 24 apples = $3.60Step 1: Find the cost of 1 apple3.6024=0.15\frac{3.60}{24} = 0.15So, 1 apple costs $0.15.Step 2: Find the cost of 10 apples10×0.15=1.5010 \times 0.15 = 1.50✅ Final Answer: $1.50 for 10 apples.

102. A total of 300 tickets were sold for a performance of a school play. The ticket prices were $5 for each adult and $3 for each child, and the total revenue from tickets was $1,400. Solving which of the following systems of equations would yield the number of adult tickets sold, a, and the number of children's tickets sold, c?

• A. a + c = 1,4005a + 3c = 300
• B. a + c = 300 5a + 3c = 1400
• C. a + c = 3003a + 5c = 1,400
• D. a + c = 3003a + 5c = 1,400 × 2

Explanation: To solve this problem, set up the system of equations based on the information provided: a + c = 300 and 5a + 3c = 1,400. Option B correctly establishes these equations, allowing you to find the number of adult and children's tickets sold. By solving these equations simultaneously, the correct values of a = 250 and c = 50 are obtained. This results in 250 adult tickets and 50 children's tickets being sold. The other options fail to provide the correct equations, leading to inaccurate conclusions.

103. Which of the following expressions is equivalent to 2(x − 4)2 − 5x?

• A. 2x2−21x+32
• B. 2x2−21x−32
• C. 2x2−13x+32
• D. 2x2−16x−21

Explanation: To simplify 2(x − 4)2 − 5x, start by expanding the squared term: (x − 4)2 = x2 − 8x + 16. Then distribute the 2 across these terms: 2(x2 − 8x + 16) = 2x2 − 16x + 32. Next, subtract 5x, resulting in 2x2 − 16x + 32 − 5x. Combine the like terms −16x and −5x to get 2x2 − 21x + 32. This matches option A, which is the correct answer. Option B incorrectly simplifies the constant term as negative. Option C has an incorrect x coefficient, and option D has errors in both the x coefficient and constant term.

104. The centre of the circle concentric with the circle x2 + y2 - 2x + 4y - 1 = 0 is:

• A. (2, -1)
• B. (-1, 2)
• C. (1, - 2)
• D. (-1, -2)

Explanation: To find the center of the circle given by the equation x2 + y2 - 2x + 4y - 1 = 0, we compare it with the standard form (x - h)2 + (y - k)2 = r2. The coefficients of x and y are -2 and 4, respectively. This means:The x-term is -2x, which gives us -2g = -2, hence g = 1.The y-term is 4y, which gives us -2f = 4, hence f = -2.Thus, the center of the circle is (1, -2), which is option C. The other options do not satisfy these computations, as they either have incorrect signs or incorrect values derived from the coefficients.

105. If n is an odd integer, which one of the following is an even integer?

• A. n3
• B. n/4
• C. 2n+3
• D. n(n+3)

Explanation: A is incorrect as assuming our odd integer is 3, cube of 3 is equal to 9, which is not even. B is incorrect as assuming our odd integer is 3, 3/4 is equal to 0.75, which is not even or neither an integer. C is incorrect as assuming our odd integer to be 3, {2(3) + 3 = 9}, which is not even, D is correct as assuming our odd integer to be 3, {3(3)+3 = 12}, which is even and an integer.

106. Which of the following fractions is the largest in the group?

• A. 7/9
• B. 2/3
• C. 5/6
• D. 13/18

Explanation: A is incorrect as 7/9 = 0.7777 B is incorrect as 2/3 = 0.6666 C is correct as 5/6 = 0.8333 0.833 is the biggest fraction compared to the other options. D is incorrect as 13/18 = 0.72222

107. If the unit digit of integer n is greater than 2, what is the unit digit of n ? (1) The units digit of n is the same as the units digit of n2(2) The units digit of n is the same as the units digit of n3

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question
• C. Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
• D. Each statement alone is sufficient
• E. Statements (1) and (2) together are not sufficient, and additional data is needed to answer the question

Explanation: A,B,C,D are incorrect as there isn't enough data given for statement 1 and statement 2 to have context. Thus, they are both not sufficient enough to draw any conclusion. E is correct as we are not given enough data to draw a conclusion and statement 1 and 2 don't suffice.

108. If sum of five prime numbers is even the smallest of the numbers is:

• A. 1
• B. 2
• C. 7
• D. 11

Explanation: A is incorrect as 1 is not a prime number. B is correct as 2 is the smallest prime number and its even. C is incorrect as its odd and not the smallest prime number. D is incorrect as its odd and its also not the smallest prime number.

109. If we subtract 2 from tenth digit of a number the new number will become:

• A. Less than 2 from original number
• B. Less than 20 from original number
• C. More than 200 from original number
• D. More than 20 from original number

Explanation: Assuming our number to be 124, subtracting 2 from the tenth digit {2} will give us the answer 104, hence B is correct since 104 us 20 less from 124. A, C, D are incorrect as the statements are wrong.

110. 6 hours are what part of 2 days:

• A. 8th
• B. 24th
• C. 12th
• D. 6th

Explanation: A is correct since there are 24 hours in one day, 48 hours in 2 days. To obtain the fraction of 6 hours against 48 hours, 48/6 = 8th. Hence, B, C, D are wrong since 6 hours are 8th part of 48 hours.