x multiple of y

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Baldini: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon Mar 02, 2009 6:06 am; Thanked: 3 times

by Baldini » Sun Mar 29, 2009 11:06 pm

If x and y are integers greater than 1, is x a multiple of y?

1. 3y^2 + 7y = x
2. x^2 – x is a multiple of y

Can someone please explain why the OA is A and not D?

Many thanks in advance

GMAX

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Source: Beat The GMAT — Data Sufficiency | Sun Mar 29, 2009 11:06 pm

bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Mon Mar 30, 2009 12:43 am

Statement 1:

3y^2 + 7y = x
y(3y + 7) = x
3y + 7 = x/y

Since y is a positive integer, then x/y = 3y+7 must be an integer, so x is a mulitple of y. Sufficient.

Statement 2:

x^2 - x = ky (where k is some positive integer 1,2,3,…)
x(x-1) = ky
x/y = k/(x-1)

If x=y=2 and k=1, then x is a multiple of y.
If k = 2, x = 4, y = 6, then x is not a multiple of y. Insufficient.

Choose A.

-BM-

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