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If a and b are integers, is a + b divisible by 15?

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by AAPL » Mon Oct 30, 2017 9:36 am
If a and b are integers, is a+b divisible by 15?

(1) a+b is divisible by 30.

(2) a+b is divisible by 5.

The OA is A.

I need help to solve this DS question. Please, can any expert explain it for me? Thanks.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Mon Oct 30, 2017 9:59 pm
AAPL wrote:If a and b are integers, is a+b divisible by 15?

(1) a+b is divisible by 30.

(2) a+b is divisible by 5.

The OA is A.

I need help to solve this DS question. Please, can any expert explain it for me? Thanks.
For a+b to be divisible by 15, it must be divisible by the prime factors of 15, ie, 3 and 5.

(1) a+b is divisible by 30.

Since the prime factors of 30 are 2, 3 and 5, a+b is divisible by 15. Sufficient.

(2) a+b is divisible by 5.

For a+b to be divisible by 15, it must be divisible by 3 too. From the statement, we are not sure whether it is also divisible by 3. Insufficient.

The correct answer: A

Hope this helps!

-Jay

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