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27 Aug 2018, 06:08
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E
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Difficulty:
75%
(hard)
Question Stats:
37% (01:25) correct
63%
(01:17)
wrong
based on 122
sessions
History
Date
Time
Result
Not Attempted Yet
Is x*y > 0?
(1) x = |y|
(2) x*|y| = x*y
(1) x = |y|
(2) x*|y| = x*y
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
27 Aug 2018, 07:39
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chetan2u
We need to find whether both x and y have same sign
Statement1:
|y| is definitely positive or 0
x is positive or 0
Insuff
Statement2:
Case 1:
x is negative and y is positive, xy>0 (False)
Case 2:
x is positive and y is positive, xy>0 (True)
Case 3:
Either x or y is 0, xy>0 (False)
Insuff
Combining both statements still we don't know whether x and y are positive or 0. Hence insuff
Hence E
27 Aug 2018, 07:40
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chetan2u
Question stem:- Is x*y > 0
St1:- x = |y| ('x' is non-negative)
So, x*y=|y|*y
Is |y|*y > 0 ?
a) When \(y\geq{0}\), |y|=y. hence \({|y|*y=y^2}\geq{0}\) (here x=|y|=y, so \(x\\
\geq{0}\))
b) When \(y<0\), |y|=-y. hence {|y|*y}<0
Question stem is inconsistent, therefore insufficient.
St2:- x*|y| = x*y
Subtracting x*y from both the sides, we have
x*|y|-x*y = x*y-x*y
Or, x*|y|-x*y=0
Or, x(|y|-y)=0 (factoring out x)
So, x=0 or |y|-y=0 (Or, |y|=y Or, \(y\geq{0}\))
a) when x=0, x*y=0
b) When y>0, x can be +ve/-ve/0. hence polarity of x*y is inconsistent.
c) When y=0, x*y=0
Insufficient.
Combined, we have \(x\geq{0}\), \(y\geq{0}\) (y<0 is excluded since it dissatisfies st2)
Here also x*y can be zero or positive.
Question stem is still inconsistent.
Ans. (E)
