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

Question

(1) x = 2p - 6

(2) 2p + 5 is divisible by 11

Bunuel · Answer

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.

Answer: C.

BN1989 · Answer

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.

subhashghosh · Answer

0 is divisible by 11, in fact by any other number than 0 itself. So the answer is C.

Abhii46 · Answer

0 when divided by 11 gives a remainder 0, hence it will be considered as divisible.
0 = 0*11 + 0.

BN1989 · Answer

Ok thanks for clearing that up.

BankerRUS · Answer

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!

Many thanks!

Bunuel · Answer

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.

BankerRUS · Answer

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.

Understood, many thanks!

BrentGMATPrepNow · Answer

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    
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

Answer: C

Cheers,
Brent

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

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

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