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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 323
sessions
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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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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
29 May 2015, 06:21
Kudos
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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 \(C\)
29 May 2015, 07:10
Kudos
Bookmarks
Ans B
Explanation :
(1) a*x^4 + a*|y| < 0
x^4+ |y| < 0
x^4 < -|y|
Assuming
x=2, y =1 -----> 16<-1 (not possible)
x=-1,y=-2 ------> 1<-2 (not possible)
x=1,y=2 -----> 1<-2 (not possible)
x=-2,y=-1 -----> 16<-1 (not possible)
or
Another way to look at this is
x^4<-|y|
on the left side of the equation the value will always be +ve
on the right side the value will always be -ve
Hence, this inequality will always be false no matter what we do.
Therefore this statement is not sufficient
(2) a*x^3 > a*y^3
x^3>y^3 (eliminating a on both sides)
The above mentioned equation is possible only when x>y
Therefore 2nd statement is sufficient.
Explanation :
(1) a*x^4 + a*|y| < 0
x^4+ |y| < 0
x^4 < -|y|
Assuming
x=2, y =1 -----> 16<-1 (not possible)
x=-1,y=-2 ------> 1<-2 (not possible)
x=1,y=2 -----> 1<-2 (not possible)
x=-2,y=-1 -----> 16<-1 (not possible)
or
Another way to look at this is
x^4<-|y|
on the left side of the equation the value will always be +ve
on the right side the value will always be -ve
Hence, this inequality will always be false no matter what we do.
Therefore this statement is not sufficient
(2) a*x^3 > a*y^3
x^3>y^3 (eliminating a on both sides)
The above mentioned equation is possible only when x>y
Therefore 2nd statement is sufficient.
