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CAT 2018 Slot 2 — QA Question 26

IndicesEasy

If N and x are positive integers such that NN = 2160 and N2 + 2N is an integral multiple of 2x, then the largest possible x is

Answer & solution

Answer: 10

Solution

From observation, NN = 2160 = 3232 or N = 32.

Now, N2 + 2N = 322 + 232 = (25 )2 + 232

= 210 + 232 = 210 (1 + 222 ).

Here, (1 + 222 ) is an odd number, hence the higest power of 2 is 10.

Therefore the largest value of x = 10.

Hence, 10.

CAT 2018 Slot 2 QA Q26: 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 — Solution | TheCATExam