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

 It is currently 16 Feb 2020, 13:22

### 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

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 p and x are integers , is x divisible by 11?

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 549
Location: PA
If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

23 Jan 2011, 07:53
1
11
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:42) correct 28% (02:04) wrong based on 279 sessions

### HideShow timer Statistics

If p and x are integers , is x divisible by 11?

(1) x = 2p - 6

(2) 2p + 5 is divisible by 11
Math Expert
Joined: 02 Sep 2009
Posts: 61189
Re: If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

23 Jan 2011, 08:01
rxs0005 wrote:
If p and x are integers , is x divisible by 11

1 x = 2p - 6

2 2p + 5 is divisible by 11

If p and x are integers, is x divisible by 11?

(1) x = 2p - 6 --> clearly insufficient: if $$p=0$$ then $$x=-6$$ and the answer will be NO but if $$p=3$$ then $$x=0$$ and the answer will be YES.

(2) 2p + 5 is divisible by 11 --> $$2p+5=11k$$ for some integer $$k$$, but this statement is also insuffcient as we know nothing about $$x$$.

(1)+(2) $$x=2p-6=2p+5-11=11k-11=11(k-1)$$ --> $$x$$ is a multiple of 11. Sufficient.

_________________
Manager
Joined: 12 Oct 2011
Posts: 105
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
Re: If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

14 Mar 2012, 06:02
If p and x are integers, is x divisible by 11?

1) x=2(p-3)
2) 2p+5 is divisible by 11

from 2) we get that p could be for example, 3, 14, 25...

if we use the value 3 in 1) we get x=0 which is not divisible by 11, and if p=14->x=22, so imo E.
Retired Moderator
Joined: 16 Nov 2010
Posts: 1210
Location: United States (IN)
Concentration: Strategy, Technology
Re: If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

14 Mar 2012, 06:10
0 is divisible by 11, in fact by any other number than 0 itself. So the answer is C.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Manager
Joined: 12 Mar 2012
Posts: 78
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Re: If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

Updated on: 14 Mar 2012, 06:17
1
0 when divided by 11 gives a remainder 0, hence it will be considered as divisible.
0 = 0*11 + 0.

Originally posted by Abhii46 on 14 Mar 2012, 06:15.
Last edited by Abhii46 on 14 Mar 2012, 06:17, edited 1 time in total.
Manager
Joined: 12 Oct 2011
Posts: 105
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
Re: If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

14 Mar 2012, 06:16
Ok thanks for clearing that up.
Intern
Joined: 16 Oct 2012
Posts: 49
If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

17 May 2013, 05:02
One question: According to the second statemet 2p could also equal -5 since 2p+5 is divisible by 11 so 2p+5 could also be zero.. if you plug it into the first statement then it is not divisible by 11 anymore. could yomeone possibly clarify this??

Many thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 61189
If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

17 May 2013, 05:19
BankerRUS wrote:

One question: According to the second statemet 2p could also equal -5 since 2p+5 is divisible by 11 so 2p+5 could also be zero.. if you plug it into the first statement then it is not divisible by 11 anymore. could yomeone possibly clarify this??

Many thanks!

We are told that p is an integer, thus 2p cannot equal to -5 because in this case p is not an integer.

Hope it's clear.
_________________
Intern
Joined: 16 Oct 2012
Posts: 49
Re: If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

17 May 2013, 05:42
We are told that p is an integer, thus 2p cannot equal to -5 because in this case p is not an integer.

Hope it's clear.[/quote]

Understood, many thanks!
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4318
Re: If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

01 May 2018, 09:55
Top Contributor
1
rxs0005 wrote:
If p and x are integers , is x divisible by 11?

(1) x = 2p - 6

(2) 2p + 5 is divisible by 11

Target question: Is x divisible by 11?

Given: p and x are integers

Statement 1: x = 2p - 6
This statement doesn't FEEL sufficient, so I'll TEST some values.
Case a: p = 10. So, x = 2(10) - 6 = 14. If x = 14, then the answer to the target question is NO; x is NOT divisible by 11
Case b: p = 14. So, x = 2(14) - 6 = 22. If x = 22, then the answer to the target question is YES; x IS divisible by 11
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2p + 5 is divisible by 11
There is no information about x.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that 2p + 5 is divisible by 11
This means that 2p+5 = 11k for some integer k

Statement 1 tells us that x = 2p - 6
My goal is to fiddle with this equation so we can use the fact that 2p+5 = 11k
Notice that we can take the equation x = 2p - 6 and REWRITE it as x = 2p + 5 - 11 [since this new equation still simplifies to be x = 2p-6]
We can now replace 2p+5 with 11k to get: x = 11k - 11
We can now factor out 11 to get: x = 11(k - 1)
This tells us that x is a MULTIPLE of 11, which also means 11 is divisible by 11
So, the answer to the target question is YES; x IS divisible by 11
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Non-Human User
Joined: 09 Sep 2013
Posts: 14074
Re: If p and x are integers , is x divisible by 11?  [#permalink]

### Show Tags

06 Nov 2019, 23:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If p and x are integers , is x divisible by 11?   [#permalink] 06 Nov 2019, 23:02
Display posts from previous: Sort by