If p is divisible by 10, then p is divisible by all of the divisors of 10 too, and in particular is divisible by 5. So Statement 1 is sufficient.

If p is not divisible by 15, then p is not divisible by (at least) one of the prime divisors of 15, so p is not divisible by (at least) one of the numbers 3 or 5. But we don't know which, so we can't answer the question - maybe p is equal to 10 and the answer is 'yes', or maybe p is equal to 11 and the answer is 'no'.

So the answer is A.
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#1
no divisible by 10 will be divisible by 5
sufficient
#2
p not divisible by 15 so
15= 3*5
p = 25 ; 5*5/3/5 ; not divisible by 15 but divisible by 5
or p = 30 , divisible by both 5 & 15
insufficient
IMO A

Hola amigos

Is the integer \(p\) divisible by \(5\) ?

1. \(p\) is divisible by \(10\)
So \(p\) is the multiple of \(10\), and \(10\) is the multiple \(5\). Thus \(p\) is the multiple of \(5\) too.
Sufficient

2. \(p\) is not divisible by \(15\)
if \(p = 20\), then it is indivisilbe by \(15\) but divisible by \(5\), so YES
if \(p = 33\), then it is indivisible by both \(15\) and \(5\), so NO
Insufficient

The answer is A

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
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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:

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