If x and y are positive integers, what is the greatest : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 19:07

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
Your Progress

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 June
Open Detailed Calendar

If x and y are positive integers, what is the greatest

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

Hide Tags

Moderator
Joined: 01 Sep 2010
Posts: 3099
Followers: 788

Kudos [?]: 6577 [13] , given: 1023

If x and y are positive integers, what is the greatest [#permalink]

Show Tags

04 Mar 2012, 06:21
13
This post received
KUDOS
32
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

41% (02:00) correct 59% (01:44) wrong based on 921 sessions

HideShow timer Statistics

If x and y are positive integers, what is the greatest common divisor of x and y?

(1) 2x + y = 73
(2) 5x – 3y = 1

[Reveal] Spoiler:
Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).

But it seems to be a trap answer......
[Reveal] Spoiler: OA

_________________

Last edited by Bunuel on 09 Jul 2014, 09:50, edited 2 times in total.
Edited the question and the OA
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93675 [30] , given: 10583

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

04 Mar 2012, 06:41
30
This post received
KUDOS
Expert's post
24
This post was
BOOKMARKED
carcass wrote:
If x and y are positive integers, what is the greatest common divisor of x and y?

1) 2x + y = 73
2) 5x – 3y = 1

MMMMMMmm

Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).

But it seems to be a trap answer......

If x and y are positive integers, what is the greatest common divisor of x and y?

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

(1) $$2x+y=73$$. Suppose GCD(x, y) is some integer $$d$$, then $$x=md$$ and $$y=nd$$, for some positive integers $$m$$ and $$n$$. So, we'll have $$2(md)+(nd)=d(2m+n)=73$$. Now, since 73 is a prime number (73=1*73) then $$d=1$$ and $$2m+n=73$$ (vice versa is not possible because $$m$$ and $$n$$ are positve integers and therefore $$2m+n$$ cannot equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient.

(2) $$5x-3y=1$$ --> $$5x=3y+1$$ --> $$5x$$ and $$3y$$ are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, $$5x$$ and $$3y$$ don't share any common factor but 1, thus $$x$$ and $$y$$ also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Answer: D.

Hope it's clear.
_________________
Moderator
Joined: 01 Sep 2010
Posts: 3099
Followers: 788

Kudos [?]: 6577 [0], given: 1023

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

04 Mar 2012, 08:22
Thanks bunuel.

From your explanation can we suppose to apply the reasoning from statement two to the first one or is not possible ?? would be a big mistake because 1 is NOT prime??'
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93675 [0], given: 10583

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

05 Mar 2012, 01:28
Expert's post
2
This post was
BOOKMARKED
carcass wrote:
Thanks bunuel.

From your explanation can we suppose to apply the reasoning from statement two to the first one or is not possible ?? would be a big mistake because 1 is NOT prime??'

I suppose you mean whether we can apply the reasoning from (1) to statement (2). Yes, we can:

(2) $$5x-3y=1$$ --> Suppose GCD(x, y) is some integer $$d$$, then $$x=md$$ and $$y=nd$$, for some positive integers $$m$$ and $$n$$. So, we'll have $$5(md)-3(nd)=d(5m-3n)=1$$ --> $$d$$ is a factor of 1, so $$d$$ must equal 1. Sufficient.
_________________
Intern
Joined: 30 Jan 2012
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

07 Apr 2012, 14:55
Hi Bunuel, Can I hire your mind for my exam...? Well if I get a good grade, a large part of it would be due to you....Thanks.

Bunuel wrote:
carcass wrote:
If x and y are positive integers, what is the greatest common divisor of x and y?

1) 2x + y = 73
2) 5x – 3y = 1

MMMMMMmm

Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).

But it seems to be a trap answer......

If x and y are positive integers, what is the greatest common divisor of x and y?

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

(1) $$2x+y=73$$. Suppose GCD(x, y) is some integer $$d$$, then $$x=md$$ and $$y=nd$$, for some positive integers $$m$$ and $$n$$. So, we'll have $$2(md)+(nd)=d(2m+n)=73$$. Now, since 73 is a prime number (73=1*73) then $$d=1$$ and $$2m+n=73$$ (vice versa is not possible because $$m$$ and $$n$$ are positve integers and therefore $$2m+n$$ can not equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient.

(2) $$5x-3y=1$$ --> $$5x=3y+1$$ --> $$5x$$ and $$3y$$ are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, $$5x$$ and $$3y$$ don't share any common factor but 1, thus $$x$$ and $$y$$ also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Answer: D.

Hope it's clear.
Manager
Joined: 17 Apr 2012
Posts: 73
GMAT Date: 11-02-2012
Followers: 3

Kudos [?]: 11 [0], given: 17

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

05 Sep 2012, 07:24
Bunuel wrote:
carcass wrote:
If x and y are positive integers, what is the greatest common divisor of x and y?

1) 2x + y = 73
2) 5x – 3y = 1

MMMMMMmm

Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).

But it seems to be a trap answer......

If x and y are positive integers, what is the greatest common divisor of x and y?

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

(1) $$2x+y=73$$. Suppose GCD(x, y) is some integer $$d$$, then $$x=md$$ and $$y=nd$$, for some positive integers $$m$$ and $$n$$. So, we'll have $$2(md)+(nd)=d(2m+n)=73$$. Now, since 73 is a prime number (73=1*73) then $$d=1$$ and $$2m+n=73$$ (vice versa is not possible because $$m$$ and $$n$$ are positve integers and therefore $$2m+n$$ can not equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient.

(2) $$5x-3y=1$$ --> $$5x=3y+1$$ --> $$5x$$ and $$3y$$ are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, $$5x$$ and $$3y$$ don't share any common factor but 1, thus $$x$$ and $$y$$ also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Answer: D.

Hope it's clear.

Hi,

Thanks for the explanation.

I m not so good in reasoning so I put the values and check.

For example in statement 1 I just entered the values of y as 1,3,5,7 and I get the values of X as 36,35,34,33 respect. After checking 4 - 5 values I got to know that the gcf is 1.

Please let me know if my strategy is good or not.

Thanks,
Manager
Joined: 09 Apr 2012
Posts: 62
Followers: 0

Kudos [?]: 53 [0], given: 27

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

05 Sep 2012, 13:04
Awesome explanation Brunnel.

Vivek, i tried to solve by plugging in numbers.
for (1) i plugged in 20,33 10,53 15, 43 and so on which satisfy the equation
and noticed that none of the pairs have any common prime factors.
So the GCF has to be 1.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7132
Location: Pune, India
Followers: 2140

Kudos [?]: 13716 [2] , given: 222

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

05 Sep 2012, 21:05
2
This post received
KUDOS
Expert's post
vivekdixit07 wrote:
Hi,

Thanks for the explanation.

I m not so good in reasoning so I put the values and check.

For example in statement 1 I just entered the values of y as 1,3,5,7 and I get the values of X as 36,35,34,33 respect. After checking 4 - 5 values I got to know that the gcf is 1.

Please let me know if my strategy is good or not.

Thanks,

Try to understand this: If something generic is established, you can plug in specific examples and use them e.g. if I say, "All boys are crazy." I can say, "Tom, a boy, is crazy."
But the other way around may not always work. From certain examples, you cannot establish something generic. e.g. I cannot say, "Tom is crazy. Alfred is crazy. Ross is crazy. We can conclude that all boys are crazy."
Here, you have tried to do something like this which is not good. We cannot blindly plug in numbers and establish that GCD will be 1. We could have missed some pairs where GCD may not have been 1. What you can do is plug in some numbers and then think why you are getting GCD = 1 in each case and whether it will be true for all pair of values.

Check out Bunuel's explanation above. It's very important and you can expect to be tested on such concepts in GMAT.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 23 Sep 2008 Posts: 24 Followers: 0 Kudos [?]: 30 [0], given: 137 Re: If x and y are positive integers, what is the greatest [#permalink] Show Tags 15 Sep 2012, 16:38 VeritasPrepKarishma wrote: vivekdixit07 wrote: Hi, Thanks for the explanation. I m not so good in reasoning so I put the values and check. For example in statement 1 I just entered the values of y as 1,3,5,7 and I get the values of X as 36,35,34,33 respect. After checking 4 - 5 values I got to know that the gcf is 1. Please let me know if my strategy is good or not. Thanks, Try to understand this: If something generic is established, you can plug in specific examples and use them e.g. if I say, "All boys are crazy." I can say, "Tom, a boy, is crazy." But the other way around may not always work. From certain examples, you cannot establish something generic. e.g. I cannot say, "Tom is crazy. Alfred is crazy. Ross is crazy. We can conclude that all boys are crazy." Here, you have tried to do something like this which is not good. We cannot blindly plug in numbers and establish that GCD will be 1. We could have missed some pairs where GCD may not have been 1. What you can do is plug in some numbers and then think why you are getting GCD = 1 in each case and whether it will be true for all pair of values. Check out Bunuel's explanation above. It's very important and you can expect to be tested on such concepts in GMAT. =============== Karishma, Bunuel, I solved the above problem in the following manner. Please let me know whether that is the right approach or not. 1) 2x+y=73=>y=73-2x As x & y are positive integers=> let x= 1 => y=71 x=2=> y=69 x=3=> y=67 => x & y have no common factors other than 1 in each cases. Sufficient 2) 5x-3y=1=> y=(5x-1)/3 As x& y are +ve integers for x= 2, y=3 x=5, y=8 x=8, y=13 => In each of the above cases, x & y have GCF=1. Sufficient ANS- D Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7132 Location: Pune, India Followers: 2140 Kudos [?]: 13716 [3] , given: 222 Re: If x and y are positive integers, what is the greatest [#permalink] Show Tags 16 Sep 2012, 22:58 3 This post received KUDOS Expert's post monsoon1 wrote: I solved the above problem in the following manner. Please let me know whether that is the right approach or not. 1) 2x+y=73=>y=73-2x As x & y are positive integers=> let x= 1 => y=71 x=2=> y=69 x=3=> y=67 => x & y have no common factors other than 1 in each cases. Sufficient 2) 5x-3y=1=> y=(5x-1)/3 As x& y are +ve integers for x= 2, y=3 x=5, y=8 x=8, y=13 => In each of the above cases, x & y have GCF=1. Sufficient ANS- D Ok, let me give you an example to show you that this approach alone is not good. Say, I change the first statement a little: 1. 2x + y = 35 As x & y are positive integers=> let x= 1 => y=33 x=2=> y=31 x=3=> y=29 x &y have GCF = 1 in each case. Does it mean they will have GCF = 1 only? What if x = 10, y = 15? These values satisfy 2x + y = 35 but the GCF is not 1. Point is, after how many values do you say that for all values GCF will be 1? Plugging in numbers can help you think straight but it may not give you the correct answer. That is why understanding the theory is important. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93675 [0], given: 10583

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

09 Jul 2013, 14:38
Bumping for review and further discussion.
_________________
Manager
Joined: 04 Jan 2014
Posts: 129
Followers: 1

Kudos [?]: 10 [0], given: 24

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

17 May 2014, 23:59
Bunuel wrote:
carcass wrote:
If x and y are positive integers, what is the greatest common divisor of x and y?

(2) $$5x-3y=1$$ --> $$5x=3y+1$$ --> $$5x$$ and $$3y$$ are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1.

Answer: D.

Hope it's clear.

Hi Bunnel,

Could you please explain how $$5x$$ and $$3y$$ are consecutive integers? I'm confused on this part.

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93675 [1] , given: 10583

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

18 May 2014, 00:29
1
This post received
KUDOS
Expert's post
pretzel wrote:
Bunuel wrote:
carcass wrote:
If x and y are positive integers, what is the greatest common divisor of x and y?

(2) $$5x-3y=1$$ --> $$5x=3y+1$$ --> $$5x$$ and $$3y$$ are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1.

Answer: D.

Hope it's clear.

Hi Bunnel,

Could you please explain how $$5x$$ and $$3y$$ are consecutive integers? I'm confused on this part.

Thanks!

$$5x=3y+1$$ means that 5x is 1 more than 3y, thus $$5x$$ and $$3y$$ are consecutive integers.

Does this make sense?
_________________
Senior Manager
Joined: 28 Apr 2014
Posts: 291
Followers: 1

Kudos [?]: 35 [0], given: 46

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

06 Jul 2014, 22:32
Maybe a silly question but how do we realize that these questions are trap questions and not simple questions. I must admit that though I got Bunuel's approach once I saw it , I will have never have been able to put that at first. During actual GMAT , I wonder if anyone will use this approach. Are there any obvious giveaways which could give a hint about thinking on different lines ? Do we have to see at what point in the exam is the question coming to be able to figure out whether it is a trap one or simple one ?
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93675 [0], given: 10583

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

07 Jul 2014, 00:12
himanshujovi wrote:
Maybe a silly question but how do we realize that these questions are trap questions and not simple questions. I must admit that though I got Bunuel's approach once I saw it , I will have never have been able to put that at first. During actual GMAT , I wonder if anyone will use this approach. Are there any obvious giveaways which could give a hint about thinking on different lines ? Do we have to see at what point in the exam is the question coming to be able to figure out whether it is a trap one or simple one ?

As I wrote both statements taken together are VERY OBVIOUSLY sufficient to answer the question. When you see such question you should be extremely cautious when choosing C for an answer.
_________________
Senior Manager
Joined: 28 Apr 2014
Posts: 291
Followers: 1

Kudos [?]: 35 [0], given: 46

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

07 Jul 2014, 01:47
Exactly Bunuel.. That was a giveaway but again that would be contextual, right. For eg in a CAT like GMAT, if this question comes as the first question, cant one be presume it to be the simplest question which GMAC is using to slowly build up the adaptive level for the test taker. Obviously if it comes at the very end and one is going great guns then the concept of CAT will kick in and one will try and figure out the trick in it

Sent from my iPhone using Tapatalk
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7132
Location: Pune, India
Followers: 2140

Kudos [?]: 13716 [0], given: 222

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

07 Jul 2014, 05:02
himanshujovi wrote:
Exactly Bunuel.. That was a giveaway but again that would be contextual, right. For eg in a CAT like GMAT, if this question comes as the first question, cant one be presume it to be the simplest question which GMAC is using to slowly build up the adaptive level for the test taker. Obviously if it comes at the very end and one is going great guns then the concept of CAT will kick in and one will try and figure out the trick in it

Sent from my iPhone using Tapatalk

I have known people to get stuck on their first or second question so I wouldn't go to the test with any presumptions. But yeah, I don't think it will be the very first question. But after 3-4 questions, all questions are fair play.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 19 Nov 2013
Posts: 27
Location: India
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 27 [0], given: 19

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

08 Jul 2014, 00:37
If 5x and 3y are consecutive, does that mean x and y will always b consecutive too?
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93675 [0], given: 10583

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

08 Jul 2014, 01:02
manish2014 wrote:
If 5x and 3y are consecutive, does that mean x and y will always b consecutive too?

No. x and y will be consecutive if x=2 and y=3 or x=-1 and y=-2. But in all other cases x and y won't be consecutive, for example, x=5 and y=8.
_________________
Senior Manager
Joined: 28 Apr 2014
Posts: 291
Followers: 1

Kudos [?]: 35 [0], given: 46

Re: If x and y are positive integers, what is the greatest [#permalink]

Show Tags

08 Jul 2014, 06:27
out of all the questions which I have encountered in my GMAT prep , this is the scariest.. Mind you not the toughest but still the scariest
Re: If x and y are positive integers, what is the greatest   [#permalink] 08 Jul 2014, 06:27

Go to page    1   2    Next  [ 36 posts ]

Similar topics Replies Last post
Similar
Topics:
1 If x and y are positive integers, what is the greatest common factor o 1 25 Oct 2016, 09:36
1 If x and y are both positive integers, what is their greatest common 7 11 Oct 2016, 01:13
2 What is the greatest common factor of the positive integers x and y? 1 6 11 Apr 2016, 03:04
19 If x, y, and z are positive integers, what is the greatest prime facto 3 30 Jan 2016, 11:08
27 If x and y are positive integers, what is the greatest 9 23 Aug 2010, 10:27
Display posts from previous: Sort by

If x and y are positive integers, what is the greatest

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.