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

Question

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.

GMATinsight · Answer

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

BrentGMATPrepNow · Answer

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

Basshead · Answer

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.

Kimberly77 · Answer

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?

BrentGMATPrepNow · Answer

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.

Kimberly77 · Answer

Understand and thanks Brent  BrentGMATPrepNow  for the clarification.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards