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:

If x and y are positive integers, what is the value of xy?

1) The greatest common factor of x and y is 10 2) the least common multiple of x and y is 180

THanks

Welcome to the Gmat Club. Below is a solution for your problem:

If x and y are positive integers, what is the value of xy?

(1) The greatest common factor of x and y is 10. Clearly insufficient as multiple values are possible for \(xy\): for instance if \(x=y=10\), \(GCF(x,y)=10\) and \(xy=100\) BUT if \(x=10\) and \(y=20\), \(GCF(x,y)=10\) and \(xy=200\).

(2) the least common multiple of x and y is 180. Also insufficient as again multiple values are possible for \(xy\): for instance if \(x=10\) and \(y=180\), \(LCM(x,y)=180\) and \(xy=1800\) BUT if \(x=1\) and \(y=180\), \(LCM(x,y)=180\) and \(xy=180\).

(1)+(2) The most important property of LCM and GCF is: for any positive integers \(x\) and \(y\), \(xy=GCF(x,y)*LCM(x,y)\), hence \(xy=GCF(x,y)*LCM(x,y)=10*180=1800\). Sufficient.

Some solutions above rely on the "property" that GCFxLCM is xy, which is nice when you know the property. Unfortunately, it is nearly impossible to learn all such properties for the GMAT. Here's a away to (try) to derive the property for this and similar problems:

GCF = 10 = 2x5 LCM = 180 = 3x3x2x2x5

The solution centers on the definition of LCM. Remember how we find LCM for two numbers? We take all the prime factors the two numbers share and multiply them by prime factors that the numbers don't share.

ie, LCM of (2x2x5x7) and (2x7x11) would be: (2x2x5x7x11)

Since we are looking for the actual product of x and y, the result will be the LCM times the factors they share (since we didn't double count them in the original LCM calculation), namely the GCF, since that's what the GCF encapsulates.

Re: If x and y are positive integers, what is the value of xy? [#permalink]

Show Tags

19 Dec 2012, 15:32

1

This post received KUDOS

This is tough.

whenever you see such question break down into factors the numbers.

So we want information to exactly calculate \(X*Y\)

1) we have 10 and the factor are 2 and 5 a bunch of numbers could have 2 and 5 in the shaded region to calculate the GCF (remembre that to obtain the GCF you take between two numbers those have the least power). Insuff

2) the same as above 180 equal \(2^2\) \(3^2\) and \(5\) but nothing more . insuff

1) and 2) for any two positive integers X and Y, \(X*Y\) \(=\) \((LCM of X and Y) x (GCF of X and Y)\). So you have: \(2*5\) from \(GCF\) and \(2^2\) \(3^2\) and \(5\) from\(LCM\). So you can calculate exactly the value of \(X*Y\)

I 'll wait from Bunuel if my explanation is correct
_________________

Re: If x and y are positive integers, what is the value of xy? [#permalink]

Show Tags

13 Jul 2014, 21:36

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.
_________________

If x and y are positive integers, what is the value of xy? [#permalink]

Show Tags

08 Nov 2014, 23:22

hello I've been trying to wrap my head around all that gcd and lcm would tell me about the numbers. When actual numbers are given it is a little easier. But when not, it gets hard, for me (like this : If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b? (1) a = 2b + 6 (2) a = 3b ------sorry about this.. i cant paste urls yet)

So I need some generalizations (so i can summarize finally )

-What do GCD and LCM tell us about the numbers? -Is it ever possible to know the numbers themselves when the LCM or GCD are given? -We found the product of numbers here. Can we find the numbers themselves in any case? Please help me, even if you know the answer to one of these questions. Also let me know if any of them don't make sense, and why. Thanks loads

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...