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29 May 2015, 05:54
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
53% (02:06) correct
47%
(02:15)
wrong
based on 321
sessions
History
Date
Time
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Not Attempted Yet
Is \(x > y\)?
(1) \(a*x^4 + a*|y| < 0\)
(2) \(a*x^3 > a*y^3\)
(1) \(a*x^4 + a*|y| < 0\)
(2) \(a*x^3 > a*y^3\)
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29 May 2015, 06:21
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Hello all
My attempt:
Statement 1:
\(a*x^4 + a*|y| < 0\)
\(a*(x^4 + |y|) < 0\)
Either \(a\) is \(-ve\) or the \(expression\) in the brackets is \(-ve\). But the \(expression\) in the bracket will always be \(+ve\) as \(x^4\) is \(+ve\) irrespective of the sign of \(x\) and \(|y|\) is always \(+ve\).
The only conclusion from this statement is that \(a\) is \(-ve\).
Therefore standalone statement 1 can't answer the question.
Statement 2:
\(a*x^3 > a*y^3\)
\(a*(x^3 - y^3) > 0\)
From this statement either \(a\) and the \(expression\) in the bracket are both \(+ve\) or both \(-ve\) so we cannot form any relationship between \(x\) and \(y\).
Therefore standalone statement 2 can't answer the question.
Combining the statement 1 & 2:
If \(a\) is \(-ve\) then as per the second statement \((x^3 - y^3)\) is also \(-ve\)
\(x^3 - y^3 <0\)
\(x^3 < y^3\)
\(x < y\)
Therefore we can answer by combining the two statements.
Hence I will go with option \(C\)
My attempt:
Statement 1:
\(a*x^4 + a*|y| < 0\)
\(a*(x^4 + |y|) < 0\)
Either \(a\) is \(-ve\) or the \(expression\) in the brackets is \(-ve\). But the \(expression\) in the bracket will always be \(+ve\) as \(x^4\) is \(+ve\) irrespective of the sign of \(x\) and \(|y|\) is always \(+ve\).
The only conclusion from this statement is that \(a\) is \(-ve\).
Therefore standalone statement 1 can't answer the question.
Statement 2:
\(a*x^3 > a*y^3\)
\(a*(x^3 - y^3) > 0\)
From this statement either \(a\) and the \(expression\) in the bracket are both \(+ve\) or both \(-ve\) so we cannot form any relationship between \(x\) and \(y\).
Therefore standalone statement 2 can't answer the question.
Combining the statement 1 & 2:
If \(a\) is \(-ve\) then as per the second statement \((x^3 - y^3)\) is also \(-ve\)
\(x^3 - y^3 <0\)
\(x^3 < y^3\)
\(x < y\)
Therefore we can answer by combining the two statements.
Hence I will go with option \(C\)
01 Jun 2015, 04:19
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Bunuel
OFFICIAL SOLUTION:
Is x > y?
(1) a*x^4 + a*|y| < 0. Factor out a: a(x^4 + |y|) < 0. Since x^4 + |y| = nonnegative + nonnegative = nonnegative, then for a*nonnegative to be negative, a must be negative. We know nothing about x and y. Not sufficient.
(2) a*x^3 > a*y^3. If a is positive, then when reducing by it, we'd get x^3 > y^3, or which is the same x > y BUT if a is negative, then when reducing by negative value and flipping the sign, we'd get x^3 < y^3, or which is the same x < y. Not sufficient.
(1)+(2) Since from (1) a < 0, then from (2) x < y. Sufficient,
Answer: C.
