GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 21 Feb 2020, 02:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

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

### Show Tags

08 Dec 2019, 23:35
00:00

Difficulty:

65% (hard)

Question Stats:

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

### HideShow timer Statistics

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

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5888
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
If m is a positive integer, is m! + (m + 1) divisible by 11?  [#permalink]

### Show Tags

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

Are You Up For the Challenge: 700 Level Questions

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.
Director
Joined: 08 Aug 2017
Posts: 696
If m is a positive integer, is m! + (m + 1) divisible by 11?  [#permalink]

### Show Tags

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
Senior Manager
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]

### Show Tags

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
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne