GMAT math question - please help!?

Question

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

(1) Greatest common factor of x and y is 10.
(2) The least common multiple of x and y is 180.

You need both statements to come up with answer. I just can't come up with it. Thanks for your help.

Answer 1

I have three sets of solutions:
10, 180
20, 90
30, 60

xy = 1800

Answer 2

GCF = 10 = 2 * 5
=> x,y have 2,5 as their common factors(1)
LCM = 180 = 2 * 3^2 * 5
=> either x or y is a multiple of 3(2)
since(1) and (2), only x or only y is a multiple of 3, otherwise they must have 3 as their common factor
thus x = 2 * 5 ; y = 2 * 5 * 3^2 , x * y = 1800 ( or x = 2 * 5 * 3^2 and y = 2 * 5)

Answer 3

Use prime factorizations.

The GCF of 10 means that the list of factors for each number will include a 2 and a 5, but no other common factors.

The LCM of 180 means that the total list of factors (excluding duplicates) will be 2, 2, 3, 3, 5

Since you know that you've excluded a 2 and a 5 (because they are the only duplicates), the factors for the product of x and y are 2, 2, 2, 3, 3, 5, 5; which multiply to 1800.

Answer 4

If you multiply the less common multiple and the greatest common factor, you will have xy.

Ana

Answer 5

gcf(x,y) . lcm(x,y) = 10 . 180 = 1800
we have a theorem that says that x.y = 1800 too.
The we don't have a unique solution for x and y. Any numbers x and y integer positive that x.y = 1800.
For example: (90,20), (18,100), (30,60) ...

Answer 6

Remember that you will have 2 min but you can think more of a due question if you think less of another one.

Remember this:

ab = mD

Ana

Answer 7

x = 10
y = 180

xy = 1800

Answer 8

xy = 1800

There is not a unique solution for x and y, but their product is unique.

Possile values for x and y are

(10,180)
(20,90)