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

[GMAT 5/18]

I think this is a prime box type question, but I have no idea how to do it.

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.

I started this question looking at statement (1). I might be wrong, but I came to the conclusion that x and y must both have 5 & 2 in their prime boxes (as this is the only way, I think, that the greatest common factor of x and y can be 10). I realised from here that I couldn't get the answer from statement (1), so that left B, C, and E.

Then, i got lost. :) Any help would be awesome. Thanks!

[Guest]

Im not too sure but the answer could be E.

Clearly 1) and 2) each by itself is insuff

Combining,
GCF=2*5
A : B
10 10
LCM=180 = 2^2*3^2*5
Since 2*5 is already allocated, now we need to split 2*3^2
This can be done two ways
A : B
1) 3^2-9 (90) : 2 (20)
2) 2*3^2=18(180): 1 (10)

So E.

[GMAT 5/18]

I guessed E as well, but the answer is C.

[dbernst]

I agree that, putting the statement together, the prime factors of 18 can be split two ways between the two prime boxes (which already contain 5*2):

Either you have 3*3*2 in one (x = 180) and y remains the same (y=10), or
you have 3*3 in one (x = 90) and 2 in the other (y = 20)

However, don't forget that the original question was What is the value of xy In either case, the value of xy = 1800. The correct answer is C.

[Live Stronger]

And also LCM(a,b) * GCD(a,b) = a*b

Stmt1 gives GCD, stmt2 gives LCM, so the answer is C

[RonPurewal]

yep.

this is pretty much all here already, including "live stronger"'s cool shortcut:

http://www.manhattangmat.com/forums/if- ... t1609.html

[abedinbhuiyan]

there must be route to go to number with prime box formula..

br

[jnelson0612]

abed, please check out the link Ron has posted. We always want to focus on the quickest, most efficient way to do a problem.

[capntangen]

What GMAT review guide would cover this topic?

[RonPurewal]

What GMAT review guide would cover this topic?

number properties