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by dnairo1981 » Thu Oct 02, 2008 5:26 pm
What is the remainder when (n-1)*(n+1) is divided by 24?
(1) When n is divided by 3, the remainder is 1.
(2) n is odd.

In understand that this has been replied to here
https://www.beatthegmat.com/good-one-t17714.html

but can someone explain why n can not be 1? Would that not mean that the three consecutive integers can be 0, 1, & 2?
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by Morgoth » Thu Oct 02, 2008 6:28 pm
As you know answer is C.

n can be 1

it satisfies both statements.
n when divided by 3 the remainder is 1
n is odd

(n-1)*(n+1) = 1-1*1+1 = 0*2 = 0

(n-1)*(n+1)/24 = 0/24 = 0

thus remainder is still 0. Sufficient.

Hope this helps.
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