If x, n, and m are positive integers and x/ n = m, is x divisible by 3?

[BTGModeratorVI]

If x, n, and m are positive integers and x/ n = m, is x divisible by 3?

(1) m is divisible by 6.
(2) n is divisible by 15.

Answer: D
Source: Manhattan Prep

[Brent@GMATPrepNow]

If x, n, and m are positive integers and x/ n = m, is x divisible by 3?

(1) m is divisible by 6.
(2) n is divisible by 15.

Answer: D
Source: Manhattan Prep

Given: x, n, and m are positive integers and x/n = m
Take: x/n = m
Multiply both sides by n to get: x = nm

Target question: Is x divisible by 3

Statement 1: m is divisible by 6
In other words, m is a multiple of 6
So, we can write: m = 6k (for some integer k)
Since we already know that x = nm, we can now replace m to write: x = (n)(6k)
Rewrite as: x = (n)(3)(2)(k)
At this point we can clearly see that x is divisible by 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is divisible by 15
In other words, n is a multiple of 15
So, we can write: n = 15k (for some integer k)
Since we already know that x = nm, we can now replace n to write: x = (15k)(m)
Rewrite as: x = (n)(3)(5)(k)(m)
At this point we can clearly see that x is divisible by 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent