Is the integer p divisible by 5 ?

AbeNeedsAnswers wrote:Is the integer p divisible by 5 ?

(1) p is divisible by 10.
(2) p is not divisible by 15.

Target question: Is the integer p divisible by 5?

Statement 1: p is divisible by 10.
If p is divisible by 10, we can write: p = 10k, for some integer k.
Rewrite this as: p = (5)(2)(k)
This tells us that p is a multiple of 5, which means p must be divisible by 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: p is not divisible by 15.
Well, there are MANY numbers that are NOT divisible by 15. Here are two:
Case a: p = 20. In this case, the answer to the target question is YES, p IS divisible by 5
Case b: p = 21. In this case, the answer to the target question is NO, p is NOT divisible by 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Hi All,

We're told that P is an integer. We're asked if P is divisible by 5. This is a YES/NO question and can be solved with Number Properties and/or TESTing VALUES.

(1) P is divisible by 10.

Since P is divisible by 10, we know that it is also a multiple of 2 and a multiple of 5. For example, P could be -20, -10, 0, 10, 20, 30, 40...etc. All of these numbers are clearly evenly divisible by 5 (since they all 'end in 0'), thus the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

(2) P is not divisible by 15.

The information in Fact 2 doesn't restrict the value of P too much (it just cannot be divisible by 15).
IF....
P = 5, then the answer to the question is YES.
P = 6, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote:Is the integer p divisible by 5 ?

(1) p is divisible by 10.
(2) p is not divisible by 15.

A

Source: Official Guide 2020

Statement One Alone:

p is divisible by 10.

We know that if integer n is divisible by integer b, then n is also divisible by any factors of b. Since p is divisible by 10, and 5 is a factor of 10, then p is also divisible by 5.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

p is not divisible by 15.

If p is 20, p/5 is an integer; however, if p = 21, then p/5 is not an integer.

Statement two alone is not sufficient to answer the question.

Answer: A