GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Jan 2019, 08:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

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

### Show Tags

Updated on: 09 Mar 2016, 04:07
2
00:00

Difficulty:

55% (hard)

Question Stats:

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

### HideShow timer Statistics

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, 03:17.
Last edited by RoberJunior on 09 Mar 2016, 04:07, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7199
Re: If x and y are non-zero integers, is x divisible by 11?  [#permalink]

### Show Tags

09 Mar 2016, 03:40
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..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: If x and y are non-zero integers, is x divisible by 11?  [#permalink]

### Show Tags

09 Mar 2016, 03:43
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
_________________
Manager
Joined: 17 Aug 2015
Posts: 99
Re: If x and y are non-zero integers, is x divisible by 11?  [#permalink]

### Show Tags

07 Feb 2017, 22:05
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, 22:05
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.