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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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Intern
Joined: 15 Mar 2016
Posts: 2
GPA: 3.6
If x, n, and m are positive integers and x/ n = m, is x divisible by 3  [#permalink]

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19 Mar 2016, 17:05
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:07) correct 20% (01:28) wrong based on 102 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.

Can someone explain this in detail please?
Math Expert
Joined: 02 Aug 2009
Posts: 7564
Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3  [#permalink]

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19 Mar 2016, 19:21
acomas 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.

Can someone explain this in detail please?

HI,

pl follow guidelines for posting a new topic..
pl Post with OA and first few letters of the Q as topic name..

info from the Q
x, n, and m are positive integers and x/ n = m
or x=n*m

lets see the statements

(1) m is divisible by 6.
x=n*m..
here m is div by 6 or m= 6* some positive integer
so x=n*6*some positive integer.

so x is div by 6 or by3
ans is YES
SUFF

(2) n is divisible by 15.
x=n*m..
here n is div by 15 or n = 15* some positive integer
so x=m*15*some positive integer.

so x is div by 15 or by 3
ans is YES
SUFF

D

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Joined: 24 May 2016
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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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03 Jun 2017, 05:13
You can also test values, for instance:
for 1) you know m/6 must be an integer and m is a multiple of 6, now plug in for x and n 12/2= 6 or 30/5=6 you will always find that x must be divisible by 3.

2) n is multiple of 15 and thus x must be divisible at least by 3 and 5 and be a multiple of 15 and thus always divisible by 3.
Director
Joined: 12 Nov 2016
Posts: 725
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
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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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19 Jul 2017, 20:04
acomas 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.

Can someone explain this in detail please?

Simple

If X/N= M then
X= M x N

and often one way of writing out divisibility and such is like if say X is divisible by 24 then X/ 3 x 2 x 2 x 2 or more usefully

x = 3 x 2 x 2 x 2 x some integer K

St 1

X= N x M

M = 3 x 2 x some integer K - therefore M is a multiple of 3 so any number that is any integer will be divisible by 3 when multiplied by M because all multiples of 6 are multiples of 3

St 2

Same logic

X = N x M

N= 5 x 3 x some integer K - so M must be a multiple of 3- multiple by N by any integer and the result will always be a multiple of 3 because multiple of 3 means made up 3's ( add 5 3's to get 15 for example)

D
Re: If x, n, and m are positive integers and x/ n = m, is x divisible by 3   [#permalink] 19 Jul 2017, 20:04
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