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# 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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CAT Sample Quantitative Ability Question Number : 1-10 | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 | 81-90 | 91-100 | 101-110 | 11-120 | 121-130 | 131-140 | 141-150 | 151-160 | 161-170 | 171-180 | 181-190 | 191-200 | 201-210 | 211-220 | 221-230 | 231-240 | 241-250
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