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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 1 of 32

1. State whether a ∈ C, if {a} ⊂ A: i: A ⊆ B ii: B ⊆ C

  • A. Statement (i) is sufficient
  • B. Statement (ii) is sufficient
  • C. Statements (i) and (ii) are each sufficient on their own
  • D. Statements (i) and (ii) together are sufficient

Explanation: Option D is correct. The chain of relationships {a} ⊂ A, A ⊆ B, and B ⊆ C allows us to conclude that a ∈ C.

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Correct answer: Statements (i) and (ii) together are sufficient

2. If 2m=4x and 2w = 8x, what is m in terms of w?

  • A. w - 1
  • B. w + 1
  • C. 2w - 1
  • D. 2w + 1

Explanation: To determine m in terms of w, we first rewrite the equations with the same base.Given: 2^m = 4x 2^w = 8xConvert 4x and 8x into powers of…

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Correct answer: w - 1

3. The sum of the Series will be i) Tn = 7n -5 ii) 𝑑 = −5 iii) 𝑎 = 2 iv) 𝑛 = 16 Which two statements are sufficient to solve the given question?

  • A. (i) and (iv)
  • B. (i) and (iii)
  • C. (ii) and (iv)
  • D. (iii) and (iv)

Explanation: The correct answer is Option A: (i) and (iv). Statement (i) provides the formula for the nth term Tn = 7n - 5, and statement (iv) gives…

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Correct answer: (i) and (iv)

4. If Lines AB||CD, then e = ?

  • A. 83
  • B. 111
  • C. 69
  • D. None

Explanation: When two lines, such as AB and CD, are parallel, and a transversal crosses them, the angles on the same side of the transversal are…

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Correct answer: 111

5. Find the number of degrees in angle B?I. AC < BCII. Angle BCD = 100°III. Angle A + Angle B + Angle C = 180°IV. AB = BCV. ABC is an isosceles triangle Which two statements are sufficient to answer the question?

  • A. I & IV
  • B. I & III
  • C. II & IV
  • D. IV & V

Explanation: Option C is correct as the information is to find the angle at B(ii) states that Angle BCD= 100° i.e Angle BCA= 180°-100° =80°(as angle on…

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Correct answer: II & IV

6. If u > t, r > q, s > t, and t > r, which of the following must be true?I. u > sII. s > qIII. u > r

  • A. I, II, and III
  • B. II only
  • C. III only
  • D. I and II
  • E. II and III

Explanation: The solution involves organizing the given inequalities to find the necessary logical relationships between variables:u > tr > qs > tt >…

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Correct answer: II and III

7. If i2k= 1, and i2= -1. Which of the following must be true about k ?

  • A. k is a multiple of 2.
  • B. k is a positive integer.
  • C. When 2k is divided by 4, the remainder is 1.
  • D. k/4 is an even integer.

Explanation: in = 1 if and only if n is a multiple of 4. (i4 = 1, i8= 1, i12 = 1, etc.) Therefore, if i2k = 1, then 2k must be a multiple of 4, and…

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Correct answer: k is a multiple of 2.

8. In the figure above, squares PQRV and VRST have sides of length 6 cm.Quantity A: The area of the shaded region PQS.Quantity B: 36cm2

  • A. Quantity A is greater.
  • B. Quantity B is greater.
  • C. The two quantities are equal.
  • D. The relationship cannot be determined from the information given.

Explanation: To find the area of the shaded region PQS, note that PQS forms a right triangle with base PQ and height QS.

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Correct answer: The two quantities are equal.

9. If x =2 and y =5 then 4x+9y =

  • A. 48
  • B. 29
  • C. 53
  • D. 40

Explanation: To solve the equation 4x + 9y when x = 2 and y = 5, substitute the values into the equation: 4(2) + 9(5).

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Correct answer: 53

10. John and Peter are hostel fellows too. Each of them pays the rent, according to their room's size. Peter's room is twice as big as John. How much rent does Peter pay if the total rent of two rooms is $600?

  • A. $600
  • B. $400
  • C. $200
  • D. $240

Explanation: To solve this, we set John's rent as $x and Peter's rent as $2x because his room is twice as big.

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Correct answer: $400

11. The average height of 10 students is 155 cm. Later on it is discovered that while calculating the average, the reading of 157 cm was wrongly read as 147 cm. The correct average is

  • A. 196
  • B. 154
  • C. 200
  • D. 156

Explanation: A, B, C are incorrect, as 156cm is the correct average height. D is correct as the total height of 10 students = 10 x 155 = 1550 cm.

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Correct answer: 156

12. Mario received y text messages each minute for 10 minutes yesterday, and received t text messages each minute for 20 minutes today. What is the total number of text messages he received for two days in terms of y and t?

  • A. 30yt
  • B. 200yt
  • C. 20y+10t
  • D. 10y+20t

Explanation: To find the total number of text messages Mario received for two days, calculate the messages for each day separately:For yesterday, with…

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Correct answer: 10y+20t

13. The sum of three-fourths of the number a and 24 is positive 9. What is the value of a ?

  • A. -44
  • B. -20
  • C. 20
  • D. 44

Explanation: The correct answer is Option B: -20.By solving the equation 3/4a + 24 = 9, we find that a = -20 after isolating the variable.

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Correct answer: -20

14. If 5(x-2)-3x=2(x-5), which of the following must be true?

  • A. x is 3
  • B. x is 4
  • C. x is 5
  • D. The equation is true for all values of x.

Explanation: The correct answer is Option D: The equation is true for all values of x.By simplifying both sides using the BODMAS rule, it can be seen…

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Correct answer: The equation is true for all values of x.

15. g(x)=kx3+3For the function g defined above, k is a constant and g(-1)=5. What is the value of g(1) ?

  • A. -3
  • B. -1
  • C. 1
  • D. 3

Explanation: To find the value of k, you can use the given condition g(-1) = 5:5 = k(-13) + 3k = -2Substitute k = -2 back into the function to find…

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Correct answer: 1

16. Which of the following is the equation of the line that passes through the point (4, -1) and has a slope −2?

  • A. x + 2y = 2
  • B. x - 2y = 6
  • C. 2x - y = 9
  • D. 2x+y=7

Explanation: The equation for the line is y=mx+cWe have the value of m = slope = -2 and it passes through point (4,-1) so, x = 4 and y = -1Substitute…

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Correct answer: 2x+y=7

17. Line L in the xy- plane contains points from each of the Quadrants I, III, and IV, but no points from Quadrant II. Which of the following must be true?

  • A. The slope of line L is zero.
  • B. The slope of line L is undefined.
  • C. The slope of line L is positive.
  • D. The slope of line L is negative.

Explanation: The correct answer is Option C. A positive slope enables the line to rise from left to right, intersecting Quadrants I, III, and IV while…

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Correct answer: The slope of line L is positive.

18. A rock climber is climbing up a 450-foot-high cliff. By 9:30 AM, the climber had reached 90 feet up the cliff, and by 11:00 AM, he had reached 210 feet up the cliff. If he climbs with a constant speed, by what time will he reach the top of the cliff?

  • A. 1:45 PM
  • B. 2:00 PM
  • C. 2:15 PM
  • D. 2:30 PM

Explanation: Constant speed is equal distance covered in equal time periods So he will cover the rest of the distance by the same time intervals as…

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Correct answer: 2:00 PM

19. Jason and Mary are running on a 200 meter track. The expressions in the table above show the distance to the finish line t seconds after they started the race. How many meters will Mary have left to finish the race when Jason is on the finish line?

  • A. 10.5 meters
  • B. 11.5 meters
  • C. 12.5 meters
  • D. 13.5 meters

Explanation: We are given two expressions that represent the distance to the finish line for Jason and Mary at time t seconds:Jason: -8t + 200Mary…

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Correct answer: 12.5 meters

20. On a map, 1 inch represents 5 miles. If a certain state is represented on a map by a rectangle 10 inches by 7.2 inches, what is the area of the state in square miles?

  • A. 360 mi2
  • B. 720 mi2
  • C. 1080 mi2
  • D. 1800 mi2

Explanation: To find the area of the state in square miles, convert the dimensions from inches to miles using the given scale.

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Correct answer: 1800 mi2
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