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n^2 - 1 is divided by 8

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n^2 - 1 is divided by 8

by sanju09 » Wed Apr 08, 2009 5:21 am
If n is a positive integer and r is the remainder when n^2 - 1 is divided by 8, what is the value of r?

(1) n is odd.

(2) n is not divisible by 8.


OA A
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by bluementor » Wed Apr 08, 2009 5:33 am
Statement 1: n is odd

n^2 - 1 = (n-1)(n+1)

therefore, (n-1) and (n+1) will form two consecutive even numbers. two consecutive even numbers are divisible by 8. hence r =0. Sufficient.

Statement 2: n is not divisible by 8

if n = 6, then r != 0.
if n = 5, then r = 0. Insufficient.

Choose A.

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