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If n = 20! + 17, then n is divisible by which of the followi
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17 Aug 2020, 10:37
17 Aug 2020, 10:37
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Question Stats:
87% (00:48) correct
12% (01:02) wrong based on 24 sessions
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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
I. 15
II. 17
III. 19
(A) None
(B) I only
(C) II only
(D) I and II
(E) II and III
Re: If n = 20! + 17, then n is divisible by which of the followi
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17 Aug 2020, 10:39
17 Aug 2020, 10:39
Expert Reply
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Re: If n = 20! + 17, then n is divisible by which of the followi
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17 Aug 2020, 10:43
17 Aug 2020, 10:43
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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
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 15
So, (15)(some number + 1) + 2 is 2 greater than a multiple of 15
So, if we divide (15)(some number + 1) + 2 by 15, the remainder will be 2
So, 20! + 17 is NOT divisible by 15
ELIMINATE 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 17
ELIMINATE 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 19
ELIMINATE E
Answer: C
Cheers,
Brent
