gmat prep remainder question

unc42 wrote:Hey I understand why "c" is the answer, but for curiousity sake I cannot actually figure out what the value of r would be and how to solve it. Any help on this?

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?

(1) 2 is not a factor of "n"
(2) 3 is not a factor of "n"

Correct answer is Both statements TOGETHER are sufficient.

Thanks for any help!

Ian Stewart wrote:

shahab03 wrote:what is the remainder when 0/24 and when 1/24?

thanks

When 0 is divided by 24, the remainder is 0 (and the quotient is 0).

When 1 is divided by 24, the remainder is 1 (and the quotient is 0).

Ian Stewart wrote:

unc42 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?

(1) 2 is not a factor of "n"
(2) 3 is not a factor of "n"

(1) says that n is odd. Thus n-1 and n+1 are both even. In fact, one of them must be divisible by 4, because every second even number is divisible by 4. So from (1) we know that (n-1)(n+1) is divisible by 8.

(2) says that n is not divisible by 3. Notice that n-1, n, and n+1 are three consecutive integers. If you have any three consecutive integers, exactly one of them must be divisible by 3. So if n is not divisible by 3, either n-1 or n+1 is.

Using both (1) and (2) together, we know (n-1)(n+1) is divisible by both 3 and 8, and therefore by 24.