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# If x and y are non-zero integers, is x divisible by 11?

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Intern
Joined: 23 Feb 2016
Posts: 1
If x and y are non-zero integers, is x divisible by 11?  [#permalink]

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Updated on: 09 Mar 2016, 05:07
2
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:36) correct 32% (02:05) wrong based on 64 sessions

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If x and y are non-zero integers, is x divisible by 11?

(1) 2x+8 = 3y
(2) 6y-5 is divisible by 11

Originally posted by RoberJunior on 09 Mar 2016, 04:17.
Last edited by RoberJunior on 09 Mar 2016, 05:07, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 6973
Re: If x and y are non-zero integers, is x divisible by 11?  [#permalink]

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09 Mar 2016, 04:40
3
RoberJunior wrote:
If x and y are non-zero integers, is x divisible by 11?

(1) 2x+8 = 3y
(2) 6y-5 is divisible by 11

Hi,
You will have to relook into the OA you have provided as E, it should be C

we know x and y are non-zero...

lets see the statements.
(1) 2x+8 = 3y
since we are looking for div of x, we should get the value of x in respect fo all other variable..
x=(3y-8)/2..
As x is an integer, y must be even..
so y=2, x=-1.. not div
y= 10, x=11.. yes div..
Insuff..

(2) 6y-5 is divisible by 11
Insuff..

combined..
from statement 2, 6y-5 is divisible by 11
so (6y-5)/11= t, where t is an integer...
so 6y=11t+5...
3y=(11t+5)/2..

substitute this value in 2x+8 = 3y
$$2x+8=\frac{(11t+5)}{2}$$..
$$4x+16=11t+5$$..
$$4x=11t-11$$..
$$4x=11(t-1)$$..
Since 4 and 11 are coprime, x must be a multiple of 11 and t-1, of 4..
Suff, as x is div by 11..
C

so the answer should be C and not E..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If x and y are non-zero integers, is x divisible by 11?  [#permalink]

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09 Mar 2016, 04:43
1
RoberJunior wrote:
If x and y are non-zero integers, is x divisible by 11?

(1) 2x+8 = 3y
(2) 6y-5 is divisible by 11

Similar question to practice: if-p-and-x-are-integers-is-x-divisible-by-108164.html
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Joined: 17 Aug 2015
Posts: 101
Re: If x and y are non-zero integers, is x divisible by 11?  [#permalink]

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07 Feb 2017, 23:05
Here is my take on this question.
2x+8 = 3y.
if x = 11, 3y = 30 and y = 10. good x and y are non zero integers and x is divisible by 11.
However if x = 2 and that will again make y =4. But x is not divisble by 11. In sufficient.

The second statement is nothing about x and so we move to combine the two statements
6y-11 is a multiple of 11 ==> 6y - 11 = 11*a where a is an integer.
now 2x+8 = 3y can be written as 4x +16=6y=> 4x+11 = 6y-5=> 4x+11 = 11*a
=> 4x = 11*a1 where a1 = a-1. again a1 is an integer
now a1= 4x/11. Since a1 is an integer and 4 isnt divisible by 11, then x must be divisible by 11.
So sufficient.
C.
Re: If x and y are non-zero integers, is x divisible by 11? &nbs [#permalink] 07 Feb 2017, 23:05
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