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

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Joined: 02 Sep 2009
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If x, n, and m are positive integers and x/ n = m, is x divisible by 3  [#permalink]

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21 Jan 2020, 03:20
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35% (medium)

Question Stats:

69% (01:11) correct 31% (01:34) wrong based on 32 sessions

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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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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3  [#permalink]

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21 Jan 2020, 05:21
1
Bunuel 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.

Given: x/ n = m i.e. x = m*n and x, m and n are integers

Question: Is x divisible by 3?

Statement 1: m is divisible by 6 = 2*3.

and x is a multiple of m i.e. x is also divisible by 3 as well hence

SUFFICIENT

Statement 2: n is divisible by 15 = 3*5

and x is a multiple of n i.e. x is also divisible by 3 as well hence

SUFFICIENT

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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3  [#permalink]

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21 Jan 2020, 06:31
Top Contributor
1
Bunuel 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.

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

Cheers,
Brent
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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3   [#permalink] 21 Jan 2020, 06:31
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