Bunuel wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy? (1) \(-4x-12y=0\) --> \(x=-3y\) --> \(x\) and \(y\) have opposite signs --> so either \(|x|=x\) and \(|y|=-y\) OR \(|x|=-x\) and \(|y|=y\) --> either \(|x|+|y|=-x+y=3y+y=4y=32\): \(y=8\), \(x=-24\), \(xy=-24*8\)
OR \(|x|+|y|=x-y=-3y-y=-4y=32\): \(y=-8\), \(x=24\), \(xy=-24*8\), same answer. Sufficient.
(2) \(|x| - |y| = 16\). Sum this one with th equations given in the stem --> \(2|x|=48\) --> \(|x|=24\), \(|y|=8\). \(xy=-24*8\) (x and y have opposite sign) or \(xy=24*8\) (x and y have the same sign). Multiple choices. Not sufficient.
Answer: A.
For hard inequality and absolute value questions with detailed solutions check this:
http://gmatclub.com/forum/inequality-an ... 39-40.htmlHope it helps.
Hi Bunuel,
I guess there's some typo because of which your second statement looks faulty.
|x|= 24 and |y| = 8
So there will be 4 different set of values of x and y (When x and y have same sign, when x and y have different sign)
The values of xy will be 42 and -42.
That is why statement 2 is not sufficient.
I guess you have missed a negative sign in one of 24*8
Let me know if I'm wrong.
_________________
You give kudos, you get kudos. :D