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# If m is a positive integer, is m! + (m + 1) divisible by 11?

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Math Expert
Joined: 02 Sep 2009
Posts: 61358
If m is a positive integer, is m! + (m + 1) divisible by 11?  [#permalink]

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08 Dec 2019, 23:35
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Difficulty:

65% (hard)

Question Stats:

48% (01:26) correct 52% (01:39) wrong based on 33 sessions

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If m is a positive integer, is $$m! + (m + 1)$$ divisible by 11?

(1) $$10 < m < 21$$
(2) m is odd

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If m is a positive integer, is m! + (m + 1) divisible by 11?  [#permalink]

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Updated on: 09 Dec 2019, 07:03
#1
10<m<21
m=11
$$m! + (m + 1)$$
m*(m-1)!+m+1
m*((m-1)!+1)+1
wont be divisible by 11 ; hence sufficient

#2
m is odd ;
m = 1 ; no
m= 3 ; no
m=9 ; yes
insufficient
IMO A

Bunuel wrote:
If m is a positive integer, is $$m! + (m + 1)$$ divisible by 11?

(1) $$10 < m < 21$$
(2) m is odd

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Originally posted by Archit3110 on 09 Dec 2019, 02:00.
Last edited by Archit3110 on 09 Dec 2019, 07:03, edited 1 time in total.
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Joined: 08 Aug 2017
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If m is a positive integer, is m! + (m + 1) divisible by 11?  [#permalink]

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09 Dec 2019, 06:33
For statement 1
Suppose M= 11
11!+(11+1) ;

11*10!+11+1

11(10!+1)+1

then how it could be divisible by 11.
Expression will not be divisible by 11 for given range of M.
Sufficient.

Archit3110 wrote:
#1
10<m<21
m=11
$$m! + (m + 1)$$
11!+(11+1) ; 11*(10!+1) /11 ; sufficient
this would be sufficient for all m= 12 ; 11*(12*10!+2) /11 ;
sufficient

#2
m is odd ;
m = 1 ; no
m= 3 ; no
m=11 ; yes
insufficient
IMO A

Bunuel wrote:
If m is a positive integer, is $$m! + (m + 1)$$ divisible by 11?

(1) $$10 < m < 21$$
(2) m is odd

Are You Up For the Challenge: 700 Level Questions
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Joined: 13 Feb 2018
Posts: 497
GMAT 1: 640 Q48 V28
Re: If m is a positive integer, is m! + (m + 1) divisible by 11?  [#permalink]

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09 Dec 2019, 08:07
1stm -- gives us a range for m
With this range m! will always be divisible by 11
So if we want the expression m!+(m+1) to be divisible by 11, then m+1 must be divisible by 11 too.
With this range, m+1 cant be divisible by 11
Sufficient

2 stm --> clearly insufficient

IMO
Ans: A
Re: If m is a positive integer, is m! + (m + 1) divisible by 11?   [#permalink] 09 Dec 2019, 08:07
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