Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 21 Oct 2016, 04:46

### 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 June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 09 Feb 2010
Posts: 70
Followers: 0

Kudos [?]: 80 [1] , given: 4

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

### Show Tags

23 Aug 2010, 11:27
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

42% (02:00) correct 58% (01:26) wrong based on 212 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: OA
Math Expert
Joined: 02 Sep 2009
Posts: 35238
Followers: 6618

Kudos [?]: 85286 [2] , given: 10236

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

### Show Tags

23 Aug 2010, 13:00
2
KUDOS
Expert's post
9
This post was
BOOKMARKED
zest4mba 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

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 since $$m$$ and $$n$$ are positve integers and therefore $$2m+n$$ cannot equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient.

(2) $$5x-3y=1$$ --> $$5x=3y+1$$. So $$5x$$ 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.

Hope it's clear.
_________________
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 404

Kudos [?]: 1435 [1] , given: 4

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

### Show Tags

23 Aug 2010, 12:58
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
zest4mba 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

Say x and y were both divisible by some number d. Then 2x + y would certainly be a multiple of d (if you add two multiples of d, you always get a multiple of d). Now we know from statement 1 that 2x + y is the number 73, so if 2x+y is divisible by d, then 73 must be divisible by d. But 73 is prime, so d could only be 1 or 73. Clearly d can't be 73, since then 2x +y would not equal 73, so the only possible value of d is 1, and thus 1 is the only common divisor of x and y.

You can use the same logic for statement 2: If x and y are both multiples of d, then 5x - 3y would need to be a multiple of d. But 5x-3y = 1, so 1 is a multiple of d, and d must be 1.

D.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Joined: 21 Jun 2014
Posts: 151
Location: United States
Concentration: General Management, Strategy
GMAT 1: 630 Q45 V31
GPA: 3.4
WE: Engineering (Computer Software)
Followers: 2

Kudos [?]: 61 [1] , given: 59

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

### Show Tags

02 Jun 2015, 04:48
1
KUDOS
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

Another way of solving it .Both x and y are integers .
From 1: x =(73-y)/2 .Since x is a integer it implies 73-y =even number .73 is Odd so y is also Odd .X is even so GCM will be 1.Sufficient

From 2 :5x-3y =1 .They are consecutive numbers i.e .odd-even or even -odd .so the GCM in this case =1 .Sufficient

Option D is correct .

Press Kudos if you like the solution.
_________________

Regards,
Manish Khare
"Every thing is fine at the end. If it is not fine ,then it is not the end "

VP
Joined: 08 Jul 2010
Posts: 1317
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 56

Kudos [?]: 1240 [1] , given: 42

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

### Show Tags

02 Jun 2015, 06:16
1
KUDOS
Expert's post
zest4mba 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

Question : GCD of x and y = ?

Statement 1: 2x + y = 73

This statement can give us multiple solutions of x and y but the important part is to notice the value of GCD in each case e.g.
(y=1, x=36) GCD = 1
(y=3, x=35) GCD = 1
(y=5, x=34) GCD = 1
(y=7, x=33) GCD = 1
(y=9, x=32) GCD = 1... and so on...

Finally we realize that instead of multiple solutions of x and y, their GCD is consistently 1,
Hence SUFFICIENT

Statement 2: 5x – 3y = 1

(y=3, x=2) GCD = 1
(y=8, x=5) GCD = 1
(y=13, x=8) GCD = 1
(y=18, x=11) GCD = 1
(y=23, x=14) GCD = 1... and so on...

Finally we realize that instead of multiple solutions of x and y, their GCD is consistently 1,
Hence SUFFICIENT

[Reveal] Spoiler:
D

Point to Learn: In all such equations with two variable you can realize that the solutions have a harmony i.e. value of variable x changes by co-efficient of y and value of y changes by co-efficient of x and this relation holds true in all such equation where the GCD of co-efficients of x and y is 1.

If there is some common factor among co-efficients of x and y then cancel the common factor and the rule holds true in those cases with modified equation.

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Feel free to give a Kudos if it is a useful post .

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 690
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 15

Kudos [?]: 147 [0], given: 15

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

### Show Tags

23 Aug 2010, 11:46
I am sure there is a clever answer to this, C obviously works... I note that from 2. X=(3y+1)/5, so y has to end in a 3 ie y= 3 13 23 etc. While x= 2 8 14 ie even, x even, can we say then that GCD = 1?

Posted from my mobile device
_________________

Consider kudos, they are good for health

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 690
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 15

Kudos [?]: 147 [0], given: 15

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

### Show Tags

23 Aug 2010, 16:01
Bunuel, Is there a complete discussion on GCDs and LCMs on the forum? Can you please point me to the same? I am trying to recollect why is x y = GCD(x,y) x LCM(x,y)? Thanks
_________________

Consider kudos, they are good for health

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12145
Followers: 538

Kudos [?]: 151 [0], given: 0

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

### Show Tags

29 Aug 2014, 13:13
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12145
Followers: 538

Kudos [?]: 151 [0], given: 0

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

### Show Tags

20 Jun 2016, 01:21
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.
_________________
Senior Manager
Joined: 02 Mar 2012
Posts: 369
Schools: Schulich '16
Followers: 3

Kudos [?]: 57 [0], given: 4

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

### Show Tags

20 Jun 2016, 05:12
manishkhare 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

Another way of solving it .Both x and y are integers .
From 1: x =(73-y)/2 .Since x is a integer it implies 73-y =even number .73 is Odd so y is also Odd .X is even so GCM will be 1.Sufficient

From 2 :5x-3y =1 .They are consecutive numbers i.e .odd-even or even -odd .so the GCM in this case =1 .Sufficient

Option D is correct .

Press Kudos if you like the solution.

just a general thing .y is odd and x is even take y =15 and x=30 .GCD N.E. 1

so there's gotta be other approach just by saying y is odd and x even won't get GCD=1 always

i guess if this type of question encounters u better skip taking a hard guess .Dont waste time(BTW gmat won't give this type of problem involving so much calculations.the paper always play with tricks which you have to find out)
Re: If x and y are positive integers, what is the greatest   [#permalink] 20 Jun 2016, 05:12
Similar topics Replies Last post
Similar
Topics:
1 If x and y are both positive integers, what is their greatest common 7 11 Oct 2016, 02:13
2 What is the greatest common factor of the positive integers x and y? 1 6 11 Apr 2016, 04:04
16 If x, y, and z are positive integers, what is the greatest prime facto 3 30 Jan 2016, 12:08
4 What is the greatest common factor of positive integers x an 3 21 Jun 2013, 22:29
91 If x and y are positive integers, what is the greatest 35 04 Mar 2012, 07:21
Display posts from previous: Sort by