Carcass wrote:
If \(n = 20! + 17\), then n is divisible by which of the following?
I. 15
II. 17
III. 19
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
Answer choice I: is 20! + 17 divisible by 15?20! + 17 = (20)(19)(18)(17)(16)(
15)(other stuff) +
15 + 2
= (
15)(some number + 1) + 2
(
15)(some number + 1) is a multiple of
15So, (
15)(some number + 1) + 2 is
2 greater than a multiple of
15So, if we divide (
15)(some number + 1) + 2 by
15, the remainder will be 2
So, 20! + 17 is NOT divisible by
15ELIMINATE B and D
Answer choice II: is 20! + 17 divisible by 17?20! + 17 = (20)(19)(18)(
17)(other stuff) +
17 = (
17)(some number + 1)
If we divide (
17)(some number + 1) by
17, the remainder will be 0
So, 20! + 17 IS divisible by
17ELIMINATE A
Answer choice III: is 20! + 17 divisible by 19?20! + 17 = (20)(
19)(other stuff) + 17
= (
19)(some number) + 17
If we divide (
19)(some number) + 17 by
19, the remainder will be 17
So, 20! + 17 is NOT divisible by
19ELIMINATE E
Answer: C
Cheers,
Brent