## Slot -2 – Quantitative Aptitude – Number System – The smallest integer n for which

The smallest integer n for which 4^n > 17^19 holds, is closest to?
a) 33

b) 35

c) 37

d) 39

Solution:
Given , 4^n > 17^19
Or  16^(n/2) > 17^19

Now from the given options, the only possible value of n is 39 as for other

values n/2 will be less than 19 and 16 < 17.

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## Slot -2 – Quantitative Aptitude – Number System – If the sum of squares of two numbers is 97

If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

a) −32

b) 16

c) 48

d) 64

Solution: let numbers are a and b.

Given, a^2+b^2=97
Using A.M.≥G.M

(a^2+b^2)/2 ≥ (a^2 b^2 )^(1/2)=ab
ab ≤ 97/2 = 48.5

Thus product of numbers can not be greater than 48.5
Option d) 64 is correct

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## Slot -1 – Quantitative Aptitude – Arithmetic – Number System – While multiplying three real numbers

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is?

Solution: Let the other two numbers are a & b so
73ab – 37ab = 720
Or 36ab = 720
ab = 20

using A.M.≥G.M
(a^2+b^2)/2 ≥(a^2 b^2 )^(1/2)=ab
(a^2+b^2) ≥2ab=40
So minimum required value = 40

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## Slot -1 – Quantitative Aptitude – Number System – The number of integers x such that 0.25

The number of integers x such that 0.25 <2x < 200, and 2x +2 is perfectly divisible by either 3 or 4, is?

Solution: as given 0.25 < 2x < 200

Or ¼ < 2x < 200

So x = { -2, -1, 0,1,2,3,4,5,6,7}

Now 2x +2 will be perfectly divisible by 3 if x is even non-negative integer and will be divisible by 4 if x = 1

So number of possible solution = 5 { x = 0, 1, 2, 4 ,6}

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a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
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