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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 111

If (h – 3) = 4h – 7, then which of the following could be the value of h?

  1. 985
  2. 784
  3. 364
  4. 2
  5. 89

Answer (d)

Explanation: The first equation is h – 3 = 4h – 7, which simplifies to h = 4/3 but this is not the answer. Let’s look at the second equation – (h – 3) = 4h – 7. This simplifies to 3 – h = 4h – 7 that means 3h = 10 and h = 2.

Question 112

If h – e > h + e, then which of the following must be true?

  1. t
  2. e < 0
  3. 25x
  4. 16
  5. 98

Answer (b)

Explanation: Algebraic manipulation is the simplest way to solve this problem. You need to add e to each side which will give inequality h > h+ 2e. Now you need to subtract from each side to get 0 > 2e and therefore the answer is (b).

Question 113

If y = cos Θ and r = sin Θ, then for all Θ, y3 + r3 =

  1. 0.45
  2. 1
  3. 8/4
  4. 4:5
  5. 32

Answer (b)

Explanation: Now put the values of y and r in the solution Sin2 Θ * Sin Θ + cos 2 Θ * cos Θ (1 – cos 2 Θ) sin Θ + (1 – sin2 Θ) cos Θ = sin Θ + cos Θ – cos 2 Θ * sin Θ - Sin2 Θ * cos Θ = (sin Θ + cos Θ) (1 - cos Θ sin Θ) Y3 + r3 = 1 Therefore the correct option is (b).

Question 114

s varies directly as the square of p. When s = 3.5, p = 0.5 If s = 90, then c would be equal to

  1. 2 √2
  2. 76
  3. 97
  4. 54
  5. 10

Answer (a)

Explanation: If s varies directly as the square of the d, it means s /p2 will always have the same value. So set up a proportion 3.5/(0.5)2 = 90/p2. You require to cross multiply and solve p2 = 8. Therefore p = 2√2

Question 115

How many different three digit numbers comprise only non-zero numbers?

  1. 765
  2. 100
  3. 674
  4. 739
  5. 564

Answer (d)

Explanation: If there is a three digit number and it has 0, then there are in fact nine possibilities for the first numbers from 1 to 9, 9 possibilities for the 2nd numbers from 1 to 9, 9th possibilities for the third number from 1 to 9. This comes to the total of 9*9*9 possible 3 digit numbers therefore the right answer is 739.

Question 116

If (h – 3) = 4h – 7, then which of the following could be the value of h?

  1. 25
  2. 14
  3. 90
  4. 2
  5. 43

Answer (d)

Explanation: The first equation is h – 3 = 4h – 7, which simplifies to m = 4/3 but this is not the answer. Let’s look at the second equation –(h – 3) = 4h – 7. This simplifies to 3 – h = 4h – 7 that means 5h = 10 and h = 2.

Question 117

If e = 2/3 and u = 6 then u/e + 4/e2 =

  1. 986
  2. 57
  3. 75
  4. 89
  5. 2346

Answer (e)

Explanation: You have to just insert the values. Insert the values given for e and u into the equation u/e + 4/e2 = 8/2 + 4/(2/3)2 = 8/2/3 + 4/4/8 = (8*3/2) + (4 * 8/4) = 18/2 + 36/4 = 9 + 9 = 18 therefore the correct answer is (d)

Question 118

If (h – 2) = 4h – 7, then which of the following could be the value of h?

  1.      876
  2. 745
  3. 89
  4.       2
  5.       78

Answer (d)

Explanation: The first equation is h – 2 = 4h – 7, which simplifies to h = 4/3 but this is not the answer. Let’s look at the second equation –(h – 2) = 4h – 7. This simplifies to 2 – h = 4h – 7 that means 5h = 10 and h = 2.

Question 119

If g = cos Θ and a = sin Θ, then for all Θ, g2 + a2 =

  1. 10
  2. 1
  3. 54
  4. 9
  5. 10

Answer (b)

Explanation: Substitute for m and c. So g2 + a2 = cos2 Θ + sin 2 Θ. But you should the correct identity of cos2 Θ + sin 2 Θ = 1. Therefore the correct option is (b)

Question 120

If log 8 = 7 then g =

  1. 7.895
  2. 87.34
  3. 1.09
  4. 87.908
  5. 0.876

Answer (c )

Explanation: The equation log 8 = 7 in exponential form, g8 = 8. Now you have to find the value of g, you are required to take the 7th root of both the sides. You will see that g = 1.09. The correct option is (c).

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