Question

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) n is not divisible by 2.
(2) n is not divisible by 3.

Answer 1

(1) n is not divisible by 2 --> pick two odd numbers: let's say 1 and 3 --> if , then and as zero is divisible by 24 (zero is divisible by any integer except zero itself) so remainder is 0 but if , then and 8 divided by 24 yields remainder of 8. Two different answers, hence not sufficient.

(2) n is not divisible by 3 --> pick two numbers which are not divisible by 3: let's say 1 and 2 --> if , then , so remainder is 0 but if , then and 3 divided by 24 yields remainder of 3. Two different answers, hence not sufficient.

(1)+(2) Let's check for several numbers which are not divisible by 2 or 3:

--> --> remainder 0;

--> --> remainder 0;

--> --> remainder 0;

--> --> remainder 0.

Well it seems that all appropriate numbers will give remainder of 0.