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Re: Data Sufficiency problem [#permalink]
14 Jun 2010, 17:12

6

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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.

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]
19 Dec 2012, 15:32

Expert's post

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 2^23^2 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 2^23^2 and 5 fromLCM. 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]
13 Jul 2014, 21:36

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