Is the integer n a multiple of 15?

[Vincen]

Is the integer n a multiple of 15?

(1) n is a multiple of 20
(2) n+6 is a multiple of 3.

The OA is C.

How can I use both statements together to determine whether n is multiple of 15 or not?

[ceilidh.erickson]

In order for an integer to be a multiple of 15, it must have factors of 3 and 5.

Target question: is n a multiple of both 3 and 5?

(1) n is a multiple of 20

This tells us that n has at least two factors of 2 and one factor of 5. Since it doesn't tell us whether it has a factor of 3, it is not enough to answer the question. Insufficient.

(2) n+6 is a multiple of 3

There is a divisibility rule that states: any multiple of a given integer x plus or minus another multiple of x will yield a multiple of x.
E.g. 10a + 15b must equal some multiple of 5 (as long as a and b are integers).

Therefore, if n + 6 = a multiple of 3, then n + [a multiple of 3] = [a multiple of 3], and therefore n must be a multiple of 3.

By itself this does not answer the full question. Insufficient.

(1) & (2) Together:
Statement (1) told us that n was a multiple of 5, and (2) told us that n was a multiple of 3. Therefore, using the statements together, n must be a multiple of both 3 and 5, i.e. 15. Sufficient.

The answer is C.

[ceilidh.erickson]

Please also POST YOUR SOURCE. It's a copyright violation to post questions without citing your source.

[ceilidh.erickson]

Vicen, following up on the above.