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

 It is currently 19 Jul 2018, 04:58

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

If x and y are positive integers greater than 1 such that x

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

Hide Tags

Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 147
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

Updated on: 15 Dec 2012, 00:30
6
00:00

Difficulty:

75% (hard)

Question Stats:

55% (01:45) correct 45% (01:30) wrong based on 476 sessions

HideShow timer Statistics

If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers?

I. x
II. x + y
III. y/x

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II and III

_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Originally posted by daviesj on 14 Dec 2012, 23:53.
Last edited by daviesj on 15 Dec 2012, 00:30, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 47109
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

15 Dec 2012, 05:38
2
5
daviesj wrote:
If x and y are positive integers greater than 1 such that x – y and x/y are both even integers, which of the following numbers must be non-prime integers?

I. x
II. x + y
III. y/x

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II and III

$$x-y=even$$ --> either both even or both odd

$$\frac{x}{y}=even$$ --> either both even or $$x$$ is even and $$y$$ is odd. Also, this statement implies that $$x>y$$.

As both statements are true --> both $$x$$ and $$y$$ must be even.

As $$\frac{x}{y}$$ is an even integer and $$y$$ is even too, then $$x$$ must be multiple of 4 (x/y=even --> x/even=even --> x=even*even).

So, we have that x>y, x is a multiple of 4 and y is even.

Only I and II will give non-prime integers, while III won't be an integer at all.

Similar question to practice: if-a-and-b-are-positive-integers-such-that-a-b-and-a-b-are-88108.html
_________________
General Discussion
Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 147
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

15 Dec 2012, 00:30
sorry...edited with right answer...:)
_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Intern
Joined: 24 Apr 2012
Posts: 48
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

16 Dec 2012, 04:22
Ans:
from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D).
_________________

www.mnemoniceducation.com

TURN ON YOUR MINDS!!!

Intern
Joined: 26 May 2012
Posts: 21
Concentration: Marketing, Technology
GMAT Date: 09-17-2012
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

16 Dec 2012, 12:20
x - y is an even integer: Therefore, for the equation to hold true, both x and y have to be even.

x/y is an even integer: Therefore, this implies that x has to be greater than y.
We can eliminate option III as y/x will never be an integer (Since x>y)

Statement I, x: x>y, hence x has to greater than 2 and even, therefore divisible by 2 and non-prime.
Statement II, x+y: x+y will be divisible by at least 2 since both x and y are even, hence the sum is non prime.

Thus, option D is the correct answer.
Math Expert
Joined: 02 Sep 2009
Posts: 47109
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

12 Jun 2013, 05:25
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Number Properties: math-number-theory-88376.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

_________________
Manager
Joined: 06 Jun 2014
Posts: 51
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

08 Apr 2016, 15:16
Hi Bunuel or any other expert...

I have a small question.
I answered E which is all 3, I got I and II, but for III of course it will be a fraction and fraction is not a prime number so I includded also III as must be true answer choice. Im I wrong or the question has to add something like a integer and non-prime, something on that line. Im sure you got my point.
Why I think this is beacuse as I remmeber well there was one OG question saying non even integer, and the correct choice was includong odd numebrs and fractions. so I got confused. I perfectly fine arrive to teh answer but this small ambiguity present in the question take away from me the correct answer.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 47109
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

09 Apr 2016, 01:50
kzivrev wrote:
Hi Bunuel or any other expert...

I have a small question.
I answered E which is all 3, I got I and II, but for III of course it will be a fraction and fraction is not a prime number so I includded also III as must be true answer choice. Im I wrong or the question has to add something like a integer and non-prime, something on that line. Im sure you got my point.
Why I think this is beacuse as I remmeber well there was one OG question saying non even integer, and the correct choice was includong odd numebrs and fractions. so I got confused. I perfectly fine arrive to teh answer but this small ambiguity present in the question take away from me the correct answer.

Thanks

Non-prime integers are integers which are not prime. Can you please share OG question you are talking about? Thank you.
_________________
Director
Joined: 26 Oct 2016
Posts: 664
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

01 Mar 2017, 18:25
Posting official solution of this problem :-
Attachments

official_5.PNG [ 101.34 KiB | Viewed 1873 times ]

_________________

Thanks & Regards,
Anaira Mitch

Non-Human User
Joined: 09 Sep 2013
Posts: 7296
Re: If x and y are positive integers greater than 1 such that x [#permalink]

Show Tags

17 Mar 2018, 22:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x and y are positive integers greater than 1 such that x   [#permalink] 17 Mar 2018, 22:47
Display posts from previous: Sort by

If x and y are positive integers greater than 1 such that x

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

Events & Promotions

 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®.