Free Quantitative Reasoning MCQs with Answers

201. Refer to the chart above. What is the Median of Exam 1?

• A. 82
• B. 84
• C. 85
• D. 79

Explanation: To determine the median, we need to arrange the numbers in ascending order. 72, 75, 77, 79, 82, 84, 85, 96, 98 Hence, the median (middle number) is 82.

202. What type of function is illustrated by the table shown?

• A. Cubic
• B. Exponential
• C. Linear
• D. Quadratic

Explanation: If the graph is plotted, it is shown to be a straight line.

203. 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
• E. y = −6x - 4

Explanation: To convert the equation 6x - 2y - 4 = 0 into slope-intercept form (y = mx + b), isolate y by moving all terms not containing y to the other side of the equation:Start with the original equation: 6x - 2y - 4 = 0.Move terms without y to the right side: -2y = -6x + 4.Divide by -2 to solve for y: y = 3x - 2.The correct answer is y = 3x - 2, with a slope of 3 and a y-intercept of -2. Option A and B have calculation errors, Option D has incorrect signs, and Option E lacks an explanation.

204. What are all the solutions for x if 3x2 - 2x-21= 0?

• A. x = -21 only
• B. x = -7 or x = 3
• C. x = -3 or x = 7/3
• D. x = -7/3 or x = -3
• E. x= 3 or x = -7/3

Explanation: Split the middle term into two terms: 3x²-9x+7x-21=0 Factor the first two terms and the last two terms separately: 3x(x-3)+7(x-3)=0 Factor out: (x-3) (3x+7)=0 Apply Zero Product Property: 2-3=0 or 3x+7=0 Rearrange unknown terms to the left side of the equation: 2 =3 Rearrange unknown terms to the left side of the equation: 3x =-7 Divide both sides of the equation by the coefficient of variable: =-7÷3 Rewrite as fraction: -3/7 Combine the results: x =3 or x=-7/3 Answer: x=3 or =- 7 /3

205. 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. (4x^2) AND (5x + 3)
• C. (4x + 2) AND (5x - 3)
• D. (4x + 3) AND (5x - 2)
• E. (4x + 3) AND (5x + 2)

Explanation: To find the factors of the quadratic equation ax2 + bx + c = 0, use the solutions x = 3/4 and x = -2/5. For each solution x = a/b, a factor is of the form (bx - a). Thus, for x = 3/4, the factor is (4x - 3), and for x = -2/5, the factor is (5x + 2). Multiplying these factors gives the original quadratic equation. Other options contain factors that do not match the solutions provided, making them incorrect.

206. The average of a list of 4 numbers is 92.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40, and the fourth number in the new list is 48. What is the average of this new list of numbers?

• A. 81.0
• B. 92.0
• C. 94.0
• D. 94.4
• E. 96.6

Explanation: As shown in the explanation As shown in the explanationWe are given:Average of original list = 92.0Number of values = 4So, sum of original list = 92.0×4=36892.0 \times 4 = 36892.0×4=368Original list: a, b, c, 40 New list: a, b, c, 48So the new list sum = 368 − 40 + 48 = 376Now, the average of the new list:376/4=94. ✅ Final Answer: 94.0

207. The arithmetic mean of the 9 consecutive integers starting with m is 24. What is the arithmetic mean of 7 consecutive integers that also start with m ?

• A. m
• B. m + 1
• C. m + 2
• D. m + 3

Explanation: The arithmetic mean of 9 consecutive integers starting with m is calculated as the middle integer, which is the 5th integer in the sequence. Therefore, the arithmetic mean is m + 4, and given that this is 24, we have m + 4 = 24, leading to m = 20. For the 7 consecutive integers starting with m, the arithmetic mean is the 4th integer, which is m + 3. Substituting m = 20, the mean is 23. Therefore, the correct answer is m + 3. Other options are incorrect as they do not align with the arithmetic mean calculation based on the sequence length provided.

208. If (3x + 2) (2x - 5) = ax2 + kx + n . What is the value of a - n + k ?

• A. 5
• B. 8
• C. 9
• D. 10
• E. 11

Explanation: Simplify LHS.. (3x+2)(2x−5)=6x2−11x−10=ax2−n+k equate the coefficients... a=6 ; k = -11 and n = -10.. so a−n+k=6−(−10)+(−11)=6+10−11=5

209. Which of the following is an equation of line l in the xy plane above?

• A. x-y=-4
• B. x-y=4
• C. x+y=-4
• D. x+y=4

Explanation: The equation x+y=-4 is correct because it matches the required slope and y-intercept of line l. Rearranging the equation yields y=-x-4, indicating a slope of -1 and a y-intercept of -4. The other options represent lines with incorrect slopes or y-intercepts, making them unsuitable for describing line l in the figure.

210. The graph of y=2x2 + 10x +12 is shown. If the graph crosses the y axis at the point (0,k), what is the value of k?

• A. 2
• B. 6
• C. 10
• D. 12

Explanation: To find where the graph crosses the y-axis, substitute x = 0 into y = 2x2 + 10x + 12. Simplifying gives y = 12, showing the intersection point as (0, 12). The correct answer is k = 12. Options 2, 6, and 10 are incorrect due to errors in substitution or calculation when x = 0 in the equation.