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Find the remainder

by pankajks2010 » Tue Jun 21, 2011 11:09 pm
If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?

a) n is not divisible by 2
b) n is not divisible by 3
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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Jun 21, 2011 11:51 pm
pankajks2010 wrote:If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?

a) n is not divisible by 2
b) n is not divisible by 3
Statement 1: n is odd.
Hence, (n - 1) and (n + 1) are even consecutive integers, i.e. one of them is divisible by 2 and the other one is by 4. Therefore we can only conclude that (n - 1)(n + 1) is divisible by 8.

Not sufficient.

Statement 2: As (n - 1), n, and (n + 1) are three consecutive integers and n is not divisible by 3, either (n - 1) or (n + 1) is divisible by 3. Therefore we can only conclude that (n - 1)(n + 1) is divisible by 3.

Not sufficient.

1 & 2 Together: (n - 1)(n + 1) is divisible by 8 and 3 and hence by 24.
Therefore, the value r is 0.

Sufficient

The correct answer is C.
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by pankajks2010 » Tue Jun 21, 2011 11:54 pm
perfect explanation..Thanks a lot!! :)
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