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Another absolute

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Another absolute

by piyush_nitt » Mon May 04, 2009 4:11 am
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

Is there any effective way to solve absolute problems?

OA: A
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Source: — Data Sufficiency |
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by 2010gmat » Mon May 04, 2009 7:08 am
1.

x = -3y;

!x! + !y! = 32 --> !-3y! + !y! = 3!y! +!y! = 32 ---> !y! = 8 --> y = + or - 8

x = - or + 24 depending on value of y but in either case product would be - 24*8 ---> suff

2. !x! - !y! = 16
+ !x! + !y! = 32 --- > 2!x! = 48 --> !x! = 24 --> x = + or - 24

Now !y! = 8 for either value of x and we will get y = + or - 8 but there can be 4 combination of xy hence 2.. is INSUFF

ans a
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