jsasipriya wrote:Is N^2-N divisible by 12 ?
1. N is divisible by 11
2. N is divisible by 19
(N² - N) = N(N - 1)
Statement 1: N is divisible by 11.
Implies (N² - N) is divisible by 11. But (N² - N) may or may not be divisible by 12 depending upon whether the product of N and (N - 1) is divisible by 12 or not. For example consider the following cases,
- 1. N = 11 => (N² - N) = N(N - 1) = 11*10 => NO
2. N = 33 => (N² - N) = N(N - 1) = 33*32 = (3*11)*(4*8) => YES
Not sufficient
Statement 2: N is divisible by 19.
Implies (N² - N) is divisible by 19. But (N² - N) may or may not be divisible by 12 depending upon whether the product of N and (N - 1) is divisible by 12 or not. For example consider the following cases,
- 1. N = 19 => (N² - N) = N(N - 1) = 19*18 => NO
2. N = 57 => (N² - N) = N(N - 1) = 57*56 = (3*19)*(4*14) => YES
Not sufficient
1 & 2 Together: N is divisible by 11 and 19. But (N² - N) may or may not be divisible by 12 depending upon whether the product of N and (N - 1) is divisible by 12 or not.
Not sufficient.
The correct answer is E.
Note: There is no need to find examples to prove the insufficiency of the statements. It's quiet obvious that N being divisible by 11 and/or 19 does not ensure that N(N - 1) is divisible by 12. I have just provided them in case there is any confusion.
