If N is a positive integer, is N! divisible by 66 ?
(1) N! is divisible by 11
(2) N! is divisible by 12
Hi, maybe I am missing something. I found this question hard.
OE
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(1) N! is divisible by 11
(2) N! is divisible by 12
Hi, maybe I am missing something. I found this question hard.
OE
[Reveal] Spoiler:
Statement (1) by itself is sufficient. For N! to be divisible by 11, N must be 11 or higher. 123...N is divisible by both 11 and 6 and thus is divisible by 66.
Statement (2) by itself is insufficient. Consider N=12 (N! is divisible by both 11 and 6 and thus is divisible by 66) and N=4 (N!=24 is divisible by 12 but is not divisible by 66).
Statement (2) by itself is insufficient. Consider N=12 (N! is divisible by both 11 and 6 and thus is divisible by 66) and N=4 (N!=24 is divisible by 12 but is not divisible by 66).
