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If a and b are non-zero integers and |a| + |b| = 32, what is ab?
(1) -4a – 12b = 0
(2) |a| – |b| = 16
(1) -4a – 12b = 0
(2) |a| – |b| = 16
21 Feb 2012, 22:09
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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: inequality-and-absolute-value-questions-from-my-collection-86939-40.html
Hope it helps.
(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: inequality-and-absolute-value-questions-from-my-collection-86939-40.html
Hope it helps.
