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Director  Joined: 07 Jun 2004
Posts: 555
Location: PA
If p and x are integers , is x divisible by 11?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 71% (01:39) correct 29% (02:01) wrong based on 324 sessions

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

(1) x = 2p - 6

(2) 2p + 5 is divisible by 11
Math Expert V
Joined: 02 Sep 2009
Posts: 58422
Re: If p and x are integers , is x divisible by 11?  [#permalink]

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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.

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GMAT 1: 700 Q48 V37 GMAT 2: 720 Q48 V40 Re: If p and x are integers , is x divisible by 11?  [#permalink]

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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.
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Re: If p and x are integers , is x divisible by 11?  [#permalink]

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0 is divisible by 11, in fact by any other number than 0 itself. So the answer is C.
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Re: If p and x are integers , is x divisible by 11?  [#permalink]

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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, 07:15.
Last edited by Abhii46 on 14 Mar 2012, 07:17, edited 1 time in total.
Manager  Joined: 12 Oct 2011
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GMAT 1: 700 Q48 V37 GMAT 2: 720 Q48 V40 Re: If p and x are integers , is x divisible by 11?  [#permalink]

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Ok thanks for clearing that up.
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If p and x are integers , is x divisible by 11?  [#permalink]

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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!
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If p and x are integers , is x divisible by 11?  [#permalink]

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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.
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Re: If p and x are integers , is x divisible by 11?  [#permalink]

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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!
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Re: If p and x are integers , is x divisible by 11?  [#permalink]

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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
_________________ Re: If p and x are integers , is x divisible by 11?   [#permalink] 01 May 2018, 10:55
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