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20! + 21 is NOT a multiple of which of the following?

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20! + 21 is NOT a multiple of which of the following?  [#permalink]

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New post 18 Oct 2017, 02:47
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (00:23) correct 28% (00:32) wrong based on 43 sessions

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\(20! + 21\) is NOT a multiple of which of the following?

I. \(21\)

II. \(7\)

III. \(2\)

A. I only
B. III only
C. I and II
D. I and III
E. I, II, and III

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Re: 20! + 21 is NOT a multiple of which of the following?  [#permalink]

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New post Updated on: 18 Oct 2017, 03:25
B

Cz in case I 21 can be taken common from 21 and 20! And in case of II 7 can be taken common from 21 and 20!

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Originally posted by 0akshay0 on 18 Oct 2017, 03:00.
Last edited by 0akshay0 on 18 Oct 2017, 03:25, edited 1 time in total.
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Re: 20! + 21 is NOT a multiple of which of the following?  [#permalink]

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New post 18 Oct 2017, 03:21
B, III only.

III is pretty easy.
The product of 20! will be even, so adding 21 to it makes it odd. Hence, not a product of 2.

I and II are a little trickier
The product of 20! will be divisible by 7 and 21, as both of those quantities can be pulled out of the factors of 20!. (i.e. 7 and 14*3 give us what we need) Adding 21 to 20! keeps those same factors, since 21 is divisible by both 7 and 21.

This means 7 and 21 are both factors of "20!+21" leaving only 2 as a non factor
Re: 20! + 21 is NOT a multiple of which of the following? &nbs [#permalink] 18 Oct 2017, 03:21
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20! + 21 is NOT a multiple of which of the following?

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