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Divisible

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by vinay1983 » Sun Oct 06, 2013 8:35 am
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.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun Oct 06, 2013 8:59 am
vinay1983 wrote: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.
Target question: Is x divisible by 3?

Given: x, n, and m are positive integers and x/n = m
This means that x = nm

Statement 1: m is divisible by 6
This means that m = 6k for some integer k
Since we already know that x = nm, we can write x = n(6k)
or x = n(2)(3)(k)
At this point, we can see that x is a multiple of 3, which means x is definitely divisible by 3.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is divisible by 15.
This means that n = 15j for some integer j
Since we already know that x = nm, we can write x = (15j)(m)
or x = (3)(5)(j)(m)
At this point, we can see that x is a multiple of 3, which means x is definitely divisible by 3.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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