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

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If x and y are positive integers, what is the value of xy? [#permalink] New post 14 Jun 2010, 16:50
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jun 2012, 04:29, edited 2 times in total.
Edited the question and added the OA
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Re: Data Sufficiency problem [#permalink] New post 14 Jun 2010, 17:12
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ctgmat123 wrote:
Can someone walk me through this one?

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.

Answer: C.

Hope it helps.
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Re: ds question [#permalink] New post 19 Oct 2010, 02:41
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satishreddy wrote:
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


This is just a formula based.

( GCFof x and y )* (LCM of x and y)= x * y

This is valid for all the numbers.Hope this will do.

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Re: Data Sufficiency problem [#permalink] New post 20 Oct 2010, 11:27
Nice, I didn't know GCF(X&Y)*LCM(X&Y)=X*Y

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lcm [#permalink] New post 24 Feb 2012, 13:14
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.

Hence, xy = LCM x GCF.

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Re: If x and y are positive integers, what is the value of xy? [#permalink] New post 19 Dec 2012, 15:32
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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 fromLCM. So you can calculate exactly the value of X*Y

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Re: If x and y are positive integers, what is the value of xy? [#permalink] New post 19 Dec 2012, 16:07
I think answer should be C as the property is GCF (x,y) * LCM(x,y) = Product of the two numbers
Hence value of xyv= 10*180= 1800

To prove A as insufficient you can plug numberssay X = 10 , Y = 30 GCF =10 product = 300 Another case X = 10 Y = 10 Hence product = 100

To prove B as insufficient you can plug in numbers X= 90 Y = 180 , Another case X=1 Y = 180
Hence Insufficient

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Re: If x and y are positive integers, what is the value of xy? [#permalink] New post 13 Jul 2014, 21:36
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Re: If x and y are positive integers, what is the value of xy?   [#permalink] 13 Jul 2014, 21:36
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