sid3699 wrote:

Could someone please explain the answer. Thanks.

If n is a postive integer and r is the remainder when (n+1)(n-1) is divided by 24, what is the value of r?

(1) n is not divisible by 2

(2) n is not divisible by 3

Edited by Gmat Tiger (GT): No OA with the question; post OA only after 4/5 responses.

individually n is not divisible by 2=>

n belongs to 3, 5,7,9,11,13,15,17,19,................ (odd numbers)

n^2-1:8,24,48,80.

so r can be 0 or non-zero. hence not sufficient.

(2) n belongs to the series:

2,4,5,7,8,10,11,13,...........

n^2-1:3,15,24,48,63,

again remainder is not determinate. hence not sufficient.

(1) & (2) together define the following series:

5,7,11,13,17,19,23,25,29,31,35,37,..............

n^2-1:24,48,120,168,.......

hence sufficient.

Hence, answer C.

I have perhaps proved this whole thing; but anyone has an easier way?

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tusharvk