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 11Case 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 11Since we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2p + 5 is divisible by 11There 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 = 11kNotice 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 11So,

the answer to the target question is YES; x IS divisible by 11Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com