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

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Manager
Joined: 07 Jun 2017
Posts: 174
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
20! + 21 is NOT a multiple of which of the following?  [#permalink]

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18 Oct 2017, 01:47
00:00

Difficulty:

25% (medium)

Question Stats:

73% (00:57) correct 27% (01:05) wrong based on 45 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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Senior Manager
Joined: 19 Apr 2016
Posts: 274
Location: India
GMAT 1: 570 Q48 V22
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GPA: 3.5
WE: Web Development (Computer Software)
Re: 20! + 21 is NOT a multiple of which of the following?  [#permalink]

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Updated on: 18 Oct 2017, 02:25
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, 02:00.
Last edited by 0akshay0 on 18 Oct 2017, 02:25, edited 1 time in total.
Joined: 15 May 2017
Posts: 197
Re: 20! + 21 is NOT a multiple of which of the following?  [#permalink]

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18 Oct 2017, 02:21
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, 02:21
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