MGMAT equations problem

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mleviko: Senior | Next Rank: 100 Posts; Posts: 63; Joined: Sun May 20, 2007 10:29 am; Thanked: 3 times

MGMAT equations problem

by mleviko » Tue Apr 15, 2008 10:27 am

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

Smashed the GMAT: 760

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 15, 2008 10:27 am

simplyjat: Master | Next Rank: 500 Posts; Posts: 423; Joined: Thu Dec 27, 2007 1:29 am; Location: Hyderabad, India; Thanked: 36 times; Followed by:2 members; GMAT Score:770

by simplyjat » Tue Apr 15, 2008 11:33 am

(1) -4x – 12y = 0 SUFFICIENT
or x + 3y = 0, or x = -3y. So we know that x and y will have different signs. And the result will be -1*|x|*|y|. Solve the equations to get |x| = 24 and |y| = 8, thus making xy = -192

(2) |x| – |y| = 16 INSUFFICIENT
we will be able to calculate |x| = 24 and |y| = 8. but the result can be -192 or 192

simplyjat