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# Is x*y > 0? (1) x = |y| (2) x*|y| = x*y

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Math Expert
Joined: 02 Aug 2009
Posts: 7764
Is x*y > 0? (1) x = |y| (2) x*|y| = x*y  [#permalink]

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27 Aug 2018, 06:08
1
4
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Difficulty:

85% (hard)

Question Stats:

39% (01:29) correct 61% (01:18) wrong based on 103 sessions

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Is x*y > 0?

(1) x = |y|
(2) x*|y| = x*y

_________________
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Joined: 17 Jan 2017
Posts: 300
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: Is x*y > 0? (1) x = |y| (2) x*|y| = x*y  [#permalink]

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27 Aug 2018, 07:39
1
chetan2u wrote:
Is x*y > 0?

(1) x = |y|
(2) x*|y| = x*y

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
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Re: Is x*y > 0? (1) x = |y| (2) x*|y| = x*y  [#permalink]

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27 Aug 2018, 07:40
chetan2u wrote:
Is x*y > 0?

(1) x = |y|
(2) x*|y| = x*y

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)
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Re: Is x*y > 0? (1) x = |y| (2) x*|y| = x*y  [#permalink]

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02 Sep 2018, 09:24
chetan2u wrote:
Is x*y > 0?

(1) x = |y|
(2) x*|y| = x*y

(1) x = |y|

case 1 -- x=0
case 2 --- x = +ve

insufficient

(2) x*|y| = x*y

case 1 --- y=0
case 2 ---y = +ve

insufficient

using both

xy=0
xy>0

insufficient
Re: Is x*y > 0? (1) x = |y| (2) x*|y| = x*y   [#permalink] 02 Sep 2018, 09:24
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# Is x*y > 0? (1) x = |y| (2) x*|y| = x*y

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