## Slot -2 – Quantitative Aptitude – Algebra – Inequalities – If N and x are positive integers

If N and x are positive integers such that N^N = 2^160 and N^2 + 2^N is an integral multiple of 2^x, then the largest possible x is?

Solution: N^N = (2^5)^32
N^N = 32^32
N=32
32^2 + 2^32 = (2^5)^2 + 2^32
32^2 + 2^32 = 2^10 + 2^32
32^2 + 2^32 = 2^10(1 + 2^22)
Hence, Largest possible value of x is 10.

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## Slot -2 – Quantitative Aptitude – Algebra – Inequalities – The smallest integer n such that n^3

The smallest integer n such that n^3 – 11n^2 + 32n – 28 > 0 is?

Solution:
Given, n^3 – 11n^2 + 32n – 28 > 0
(n-7) (n-2)^2>0

Therefore n must be greater than 7.
So smallest integral value of n = 8

## Online Coaching Course for CAT Exam Preparation

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