non zero integers

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gmatnmein2010: Master | Next Rank: 500 Posts; Posts: 185; Joined: Thu Feb 04, 2010 3:06 am; Thanked: 6 times

by gmatnmein2010 » Fri Feb 19, 2010 7:59 pm

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

(1) -4x - 12y = 0

(2) |x| - |y| = 16

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Source: Beat The GMAT — Data Sufficiency | Fri Feb 19, 2010 7:59 pm

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Fri Feb 19, 2010 9:22 pm

gmatnmein2010 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Fri Feb 19, 2010 9:37 pm

gmatnmein2010 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16

IMO A

(1) -4x-12y=0 --> x+3y=0 --> x=-3y --> x and y have opposite signs --> either |x|+|y|=-x+y=3y+y=4y=32: y=8 x=-3, xy=-24 OR |x|+|y|=x+(-y)=-3y-y=-4y=32: y=-8, x=3, xy=-24. The same answer. Sufficient.

(2) Multiple choices. Not sufficient.

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sun Feb 21, 2010 1:04 am

gmatnmein2010 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16

|x| + |y| = 32 represnts area bounded by four lines x+y=32, x-y=32, -x+y =32, -x-y=32.
St.1 : -4x-12y = 0 --> x=-3y
so |-3y | + |y| = 32 --> |4y| = 32 --> y = =+/-8
if y = 8 , x = -24 xy = -192
if y =-8, x=24 xy =-192
so we get xy =-192 hence suff.
St.2 |x| - |y| = 16 is the area bounded by lines x+y =16, x-y =16 , -x+y =16, -x-y =16 ....so it s a rectangle which conatins many points...
hence not sufficient to calculate xy

Ans A

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