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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: If x and y are positive integers, what is the greatest [#permalink]
23 Aug 2010, 10:46
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?
Re: If x and y are positive integers, what is the greatest [#permalink]
23 Aug 2010, 11:58
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
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
Re: If x and y are positive integers, what is the greatest [#permalink]
23 Aug 2010, 12:00
Expert's post
6
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 \(2m+n\) can not 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.
Re: If x and y are positive integers, what is the greatest [#permalink]
23 Aug 2010, 15:01
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 _________________
Re: If x and y are positive integers, what is the greatest [#permalink]
29 Aug 2014, 12:13
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. _________________
Re: If x and y are positive integers, what is the greatest [#permalink]
02 Jun 2015, 03:48
1
This post received 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 "
Re: If x and y are positive integers, what is the greatest [#permalink]
02 Jun 2015, 05:16
1
This post received 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
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.
Classroom Centre Address: GMATinsight 107, 1st Floor, Krishna Mall, Sector-12 (Main market), Dwarka, New Delhi-110075 ______________________________________________________ Please press the if you appreciate this post !!
gmatclubot
Re: If x and y are positive integers, what is the greatest
[#permalink]
02 Jun 2015, 05:16
The “3 golden nuggets” of MBA admission process With ten years of experience helping prospective students with MBA admissions and career progression, I will be writing this blog through...
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...