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01 Oct 2018, 04:43
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (02:29) correct
71%
(02:32)
wrong
based on 143
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y are non-zero integers, what is the value of \((x^{2y} − 1)\)?
(1) \(|x|+|y|=5\), where \(1 < |x| < y\)
(2) \(|x^2 − 4|+|y − 3| = 0\)
(1) \(|x|+|y|=5\), where \(1 < |x| < y\)
(2) \(|x^2 − 4|+|y − 3| = 0\)
01 Oct 2018, 05:01
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Bunuel
Question: what is the value of \((x^{2y} − 1)\)?
To answer the question we need to know the value of \(x^y\) irrespective of the sign of this expression because we finally have to square it to calculate \((x^{2y} − 1)\)
Statement 1: \(|x| + |y| = 5\), where \(1 < |x| < y\)
This statement is Possible only when \(x = +2\) or \(-2\) and \(y = +3\)
i.e. \(x^y = 2^3 or -2^3 = +8 or -8\)
i.e. \(x^{2y} = 8^2 = 64\)
SUFFICIENT
Statement 2: \(| x^2 − 4| + | y − 3| = 0\)
Since modulus of any expression can't be Negative hence minimum it may be zero
therefore in this case \(| x^2 − 4| \) and \(| y − 3| \) both MUST be zero
i.e. \(x = +2\) or \(-2\) and \(y = 3\)
i.e. \(x^y = 2^3 or -2^3 = +8 or -8\)
i.e. \(x^{2y} = 8^2 = 64\)
SUFFICIENT
Answer: Option D
P.S.This is GMATINSIGHT Method taught at GMATINSIGHT class which is so logical and so quick that any mathematical solutionmay be left behind. To know more, you may get in touch.
08 Oct 2018, 01:35
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GMATinsight
i understand the secondstatement explanation,but unable to understand 1 statement:
This statement is Possible only when \(x = +2\) or \(-2\) and \(y = +3\)
Why cannot we consider x=-3 and y=-2
or x=3 and y=-3
