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GMAT math question - please help!?

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.

8 Answers

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  • 1 decade ago
    Favorite Answer

    I have three sets of solutions:

    10, 180

    20, 90

    30, 60

    xy = 1800

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  • 1 decade ago

    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)

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  • Tim P.
    Lv 5
    1 decade ago

    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.

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  • 1 decade ago

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

    Ana

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  • 1 decade ago

    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) ...

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  • 1 decade ago

    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

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  • Dave
    Lv 6
    1 decade ago

    x = 10

    y = 180

    xy = 1800

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  • 1 decade ago

    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)

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