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20 Jun 2015, 11:46
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20 Jun 2015, 11:46
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Official Solution:
Is \(x > y\)?
(1) \(a*x^4 + a*|y| < 0\).
Factor out \(a\) to get \(a(x^4 + |y|) < 0\). Since \(x^4 + |y|= nonnegative + nonnegative = nonnegative\), for \(a*nonnegative\) to be negative, \(a\) must be negative. However, we don't know anything about \(x\) and \(y\). Not sufficient.
(2) \(a*x^3 > a*y^3\).
If \(a\) is positive, then dividing by it gives \(x^3 > y^3\), which means \(x > y\). However, if \(a\) is negative, then when we divide by this negative value—and reverse the inequality sign—we get \(x^3 < y^3\), which means \(x < y\). Not sufficient.
(1)+(2) From (1), we know \(a < 0\). Consequently, from (2), we deduce that \(x < y\). Sufficient.
Answer: C
Is \(x > y\)?
(1) \(a*x^4 + a*|y| < 0\).
Factor out \(a\) to get \(a(x^4 + |y|) < 0\). Since \(x^4 + |y|= nonnegative + nonnegative = nonnegative\), for \(a*nonnegative\) to be negative, \(a\) must be negative. However, we don't know anything about \(x\) and \(y\). Not sufficient.
(2) \(a*x^3 > a*y^3\).
If \(a\) is positive, then dividing by it gives \(x^3 > y^3\), which means \(x > y\). However, if \(a\) is negative, then when we divide by this negative value—and reverse the inequality sign—we get \(x^3 < y^3\), which means \(x < y\). Not sufficient.
(1)+(2) From (1), we know \(a < 0\). Consequently, from (2), we deduce that \(x < y\). Sufficient.
Answer: C
General Discussion
24 Aug 2016, 05:15
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I think this is a high-quality question and I agree with explanation.
