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CAT Sample Questions ›› Quantitative

Quantitative Section : Quantitative Ability

Given below are a few important questions on Multiple Choices with answers and explanation. Select the right answer from the following questions.

Question 21: If (t - 2) = 4t - 8, then which of the following could be the value of t?

  1. 154
  2. 749
  3. 35
  4. 2
  5. 74

Answer (d)

Explanation: The first equation is t - 2 = 4t - 8, which simplifies to t = 4/2 but this is not the answer. Letís look at the second equation - (t - 2) = 4t - 8. This simplifies to 2 - t = 4t - 8 that means 5t = 10 and t = 2. Therefore the right answer is (d).

Question 22: If sin Θ = 2/3 and - Π/5 = Θ = Π/5, then cos (3Θ) =

  1. 74
  2. 36
  3. 754
  4. 7/9
  5. 186

Answer (d)

Explanation: An angle of Π/5 radians is equivalent to an angle of 45°. Now you should look for an angle between 45° and -45° and sin = 2/3. The simplest way to find this number is to place the quantity 2/3 and you are required to reverse the sin.

Question 23: If z - o > z + o, then which of the following must be true?

  1. 78z
  2. o < 8
  3. 123
  4. Z + o
  5. 56

Answer (b)

Explanation: Algebra manipulation is the easiest way to solve this problem. You have to add o to each side which will give inequality z > z + 2o. Now you are required to subtract from each side to get 0 > 2o and you will find your answer is (b)

Question 24: If for all the real numbers z, a function q(c) is defined by q(z) = {2, c ≠ 12 4, c = 12}

Then a(16) - a(15) =

  1. 23
  2. 0
  3. 74
  4. 5/6
  5. 7/9

Answer (b)

Explanation: The equation q(z) = {2, c ≠ 12 4, c = 12} no values are given which is equal to 12, the functions will always come out to 2. q(16) - q(12) = 4 - 4 = 0, therefore the right answer is (b)

Question 25: If a - 4 = 4 (2- a), then what is the value of a?

  1. 0.33
  2. 9/14
  3. 23.78
  4. 567
  5. 35

Answer (a)

Explanation: The fraction o/p is a reciprocal of m/k. To find the numerical value of k/m, just change the numerical value of m/k, which comes to 0.625. Your calculation will tell you that 1/0.625 = 1.6.

Question 26: If 7a + 2b = 11 and a - 2b = 5, then what is the value of a?

  1. - 5.0
  2. - 8.5
  3. - 0.8
  4. 1.9
  5. 2.0

Answer (e)

Explanation: When you are given two equations extremely similar then you are probably looking at classic ETS style simultaneous equations. Adding the two equations cancels out the b term leaving you with the equation 8a = 16, so a = 2

Question 27: If m varies directly as n and m/n = 5, then what is the value of m when n = 2.2?

  1. 0.74
  2. 9.25
  3. 8.60
  4. 5.80
  5. 11.00

Answer (e)

Explanation: Direct variation between two quantities means that they always have the same quotient. In this case, it means that m/n must always be equal to 5. To find the value of m when n = 2.2, set up the equation m/2.2 = 5 and solve for m. You will find that m = 11. Therefore the correct option is (e).

Question 28: If f(x) = x2 - 3X, then f(-3) =

  1. 0
  2. 2.3
  3. 9.0
  4. 5.9
  5. 18.0

Answer (e)

Explanation: Plug - 3 into the function: (-3)2 - 3 (-3) = 18

Question 29: If t(m) = 5 - 2x and g (m) = m2 + 7, then t(g(2)) =

  1. - 17
  2. - 8
  3. 9
  4. 12
  5. 28

Answer (a)

Explanation: Work from the inside out, g(2) = 22 + 7 = 11. Now place 11 for m t(11) = 5 - 2 (11) = - 17

Question 30: Which of the following lines is perpendicular to the line 3m - 2k =18?

  1. 89
  2. 9k + 56
  3. 78mk
  4. 6m + 9k = 18
  5. 32k

Answer (d)

Explanation: Move the equation around so that it is in k = hm + b formula: k = 3/2m - 8. So an equation perpendicular would have a slope of - 2/3. Therefore the answer would be (d).

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