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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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Bunuel
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If x, n, and m are positive integers and x/ n = m, is x divisible by 3 [#permalink] New post   21 Jan 2020, 04:20
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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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D
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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3 [#permalink] New post   21 Jan 2020, 06:21
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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

Answer: Option D
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BrentGMATPrepNow
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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3 [#permalink] New post   21 Jan 2020, 07:31
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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

Answer: D

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] New post   10 Dec 2020, 18:46
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.


x/n = m
x = nm
Is nm divisible by 3?

(1) m is divisible by 2*3.

Therefore nm is divisible by 3. SUFFICIENT.

(2) n is divisible by 3*5

Therefore nm is divisible by 3. SUFFICIENT.

Answer is D.
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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3 [#permalink] New post   23 Nov 2022, 11:43
BrentGMATPrepNow wrote:
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

Answer: D

Cheers,
Brent


Hi BrentGMATPrepNow, in St1. x = (n)(3)(2)(k). As you mentioned that At this point we can clearly see that x is divisible by 3. How about n? As we don't know n yet?
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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3 [#permalink] New post   23 Nov 2022, 20:07
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Kimberly77 wrote:

Hi BrentGMATPrepNow, in St1. x = (n)(3)(2)(k). As you mentioned that At this point we can clearly see that x is divisible by 3. How about n? As we don't know n yet?


All that matters for this question is that we need to answer the target question "Is X divisible by 3?"
Since x is clearly a multiple of 3, we can answer the target question.
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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3 [#permalink] New post   24 Nov 2022, 13:10
BrentGMATPrepNow wrote:
Kimberly77 wrote:

Hi BrentGMATPrepNow, in St1. x = (n)(3)(2)(k). As you mentioned that At this point we can clearly see that x is divisible by 3. How about n? As we don't know n yet?


All that matters for this question is that we need to answer the target question "Is X divisible by 3?"
Since x is clearly a multiple of 3, we can answer the target question.


Understand and thanks Brent BrentGMATPrepNow for the clarification.
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Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3 [#permalink] New post   12 Mar 2024, 02:04
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