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Free Quantitative Reasoning MCQs with Answers

625 Quantitative Reasoning MCQs from Analytical and Logical Reasoning, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.

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625 questions · page 7 of 32

121. Which of the following is a rational number?

  • A. √49/64
  • B. √1.6
  • C. √0.9
  • D. -√250

Explanation: A, C and D are incorrect as they are irrational. B is correct as √(49/64) = √49/√64 = ⅞ 7/8 is in the form of a/b √(49/64) is a rational…

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Correct answer: √49/64

122. What number is halfway between -5/6 and 1/3 on a number line?

  • A. -1/3
  • B. -1/4
  • C. -1/2
  • D. -5/12

Explanation: A is correct as ⅓-⅚ (not using negative sign with 5/6 beacuse if we do so then both the numbers will be added and answer will be…

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Correct answer: -1/4

123. Two and three-fifths of a number equals −26 . What is the number?

  • A. -15
  • B. -10
  • C. -5
  • D. 10

Explanation: To solve the equation 2 ⅗ * n = -26, convert the mixed number to an improper fraction: 13/5 * n = -26.

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Correct answer: -10

124. There are one hundred and forty-two students in a high school band. These students represent two ninth of the total students in the high school. How many students attend the school?

  • A. 587
  • B. 613
  • C. 639
  • D. 665

Explanation: To determine the total number of students in the high school, set up a proportion using the information that the 142 band students…

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Correct answer: 639

125. 820c+380r=4,360 The above equation models the amount of calories in a snack of c cups of cashews and r cups of raisins. The amount of calories per cup of cashews is 820 and the amount of calories per cup of raisins is 380. According to the equation, how many cups of raisins are used, if 3 cups of cashews are used to make the snack?

  • A. 3
  • B. 4
  • C. 5
  • D. 6

Explanation: Given the equation 820c+380r=4360, when c=3, substituting into the equation gives: 820(3) + 380r = 4360, 2460 + 380r = 4360, 380r = 1900…

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Correct answer: 5

126. A $48 shirts costs $22 more than one half the cost of a pair of pants. How much does the pair of pants cost?

  • A. 26
  • B. 52
  • C. 42
  • D. 88

Explanation: Let the cost of the pair of pants be x. The cost of the shirt is $48, which is $22 more than half the cost of the pants.

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Correct answer: 52

127. Twice a number n increased by 11 is the same as six times the number decreased by 9. What is the value of n?

  • A. 3
  • B. 12
  • C. 5
  • D. 18

Explanation: To solve this problem, we first translate the given information into an algebraic equation: 2n + 11 = 6n - 9.

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Correct answer: 5

128. One half of a number increased by 3 is five less than two thirds of the number. What is the number?

  • A. 58
  • B. 45
  • C. 48
  • D. 68

Explanation: To solve the problem, first translate the statement into an equation: ½n + 3 = ⅔n - 5. Simplifying this, you get n = 48.

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Correct answer: 48

129. Four times the greatest of three consecutive odd integers exceeds three times the least by 31. What is the greatest of the three consecutive odd integers?

  • A. 33
  • B. 47
  • C. 19
  • D. 61

Explanation: To solve the problem, express the three consecutive odd integers as x, x + 2, and x + 4.

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Correct answer: 19

130. 4x+13=7(x-2)+bxIf the linear equation above has no solution, which of the following could be the value of b?

  • A. -1
  • B. -2
  • C. -3
  • D. -4

Explanation: If a linear equation has the same coefficients and the same constants on opposite sides of the equation, it has no solutions.

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Correct answer: -3

131. The quotient of ,a number and five, equals nine less than one half of the number. What is the number?

  • A. -20
  • B. -10
  • C. 20
  • D. 30

Explanation: Let the number be represented as x. The equation formed is x/5 + 9 = x/2. Simplifying further, we get x = 30.

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Correct answer: 30

132. If point (7,b ) is in Quadrant I and point ( a, -3) is in Quadrant III, in which Quadrant is the point (a,b)?

  • A. Quadrant I
  • B. Quadrant II
  • C. Quadrant III
  • D. Quadrant IV

Explanation: To determine the quadrant in which the point (a, b) lies, analyze the given conditions.

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Correct answer: Quadrant II

133. What is the average rate of change for the relation shown in the table?

  • A. 1/3
  • B. 1/2
  • C. 5/6
  • D. 2/3

Explanation: To find the average rate of change, we use the formula (y2 - y1) / (x2 - x1), which represents the change in y divided by the change in x.

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Correct answer: 2/3

134. In 2005, 120 students at Lincoln High School had smartphones. By 2010, 345 students in the same school had smartphones. Which of the following best describes the annual rate of change in the number of smartphones students had from 2005 to 2010 at Lincoln High School?

  • A. The average increase in the number of smartphones per year is 40
  • B. The average increase in the number of smart phones per year is 45
  • C. The average increase in the number of smartphones per year is 50
  • D. The average increase in the number of smartphones per year is 55

Explanation: To determine the annual rate of change, calculate the difference in the number of students with smartphones from 2005 to 2010, which is…

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Correct answer: The average increase in the number of smart phones per year is 45

135. Which of the following equations represents a line that passes through point (7,6) and is parallel to the x- axis?

  • A. x=6
  • B. x=7
  • C. y=7
  • D. y=6

Explanation: A line parallel to the x-axis must have a constant y-value, as it does not rise or fall.

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Correct answer: y=6

136. y=2x+4x-y=-1Which ordered pair (x,y) satisfies the system of equations shown above?

  • A. ( -2, -3)
  • B. ( -3, -2)
  • C. ( -1, 2)
  • D. ( -2, 0)

Explanation: To solve the system of equations, substitute the values of x and y from the ordered pair into both equations.

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Correct answer: ( -3, -2)

137. Which of the following expressions is equal to −1 for some values of x?

  • A. |1-x|+6
  • B. |1-x|+4
  • C. |1-x|+2
  • D. |1-x|-2

Explanation: Option A) 1 - x = -6 1 + 6 = x x= 7 Option B) - 4=1 - x X = 5 Option C) 1 - x = -2 1 + 2 = x Option D) 1 - x =2 1 - 2 = x = -1 The correct…

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Correct answer: |1-x|-2

138. At the beginning of a trip, the tank of Chloe's car was filled with 12 gallons of gas. When she travels constantly on the highway at 60 miles per hour, the car consumes 1 gallon of gas per 35 miles. If she traveled 5 hours and 15 minutes on the highway with a constant speed of 60 miles per hour, how many gallons of gas are left in the tank?

  • A. 3
  • B. 4
  • C. 5
  • D. 6

Explanation: For this to be solved we have to find the gallons of gas used If car travels 60 miles in one hour Car uses 1 gallon for 35 miles let's…

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Correct answer: 3

139. In 2005 a house was purchased for $280,000 and in 2013 it was sold at $334,000. Assuming that the value of the house increased at a constant annual rate what will be the price of the house in the year 2018?

  • A. $354,250
  • B. $361,000
  • C. $367,750
  • D. $374,500

Explanation: To solve this problem, first determine the annual increase in the house's value between 2005 and 2013.

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Correct answer: $367,750

140. From 1990 to 2000, the population of city A rose from 12,000 to 28,000 and the population of city B rose from 18,000 to 24,000. If the population of the two cities increased at a constant rate, in what year was the population of both cities the same?

  • A. 1996
  • B. 1997
  • C. 1994
  • D. 1999

Explanation: To find the year when the populations of the two cities are equal, first calculate the annual increase in population for each city.For…

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Correct answer: 1996
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