Carcass wrote:
The factorial expression 13!7! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 9
13!7!=(13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)(7)(6)(5)(4)(3)(2)(1)=(13)(12)(11)(10)(9)(8)(13)(12)(11)(10)(9)(8) is divisible by 3, because (13)(12)(11)(10)(9)(8) = (13)(12)(11)(10)(
3)(
3)(8). Eliminate A
(13)(12)(11)(10)(9)(8) is divisible by 5, because (13)(12)(11)(10)(9)(8) = (13)(12)(11)(
5)(
2)(9)(8). Eliminate B
(13)(12)(11)(10)(9)(8) is divisible by 6, because (13)(12)(11)(10)(9)(8) = (13)(
7)(
2)(11)(10)(9)(8). Eliminate C
(13)(12)(11)(10)(9)(8) is divisible by 6, because (13)(12)(11)(10)(9)(8) = (13)(12)(11)(10)(
9)(8). Eliminate E
Answer: D
Cheers,
Brent