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# Is |x|/x > |y|/y?

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Math Expert
Joined: 02 Aug 2009
Posts: 6798

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19 May 2016, 22:35
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95% (hard)

Question Stats:

33% (01:53) correct 67% (01:08) wrong based on 212 sessions

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Is $$\frac{|x|}{x} > \frac{|y|}{y}$$, if $$xy\neq{0}$$ ?

(1) $$x<0$$
(2) $$y<0$$

slightly tricky

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Math Expert
Joined: 02 Aug 2009
Posts: 6798
Re: Is |x|/x > |y|/y?  [#permalink]

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22 May 2016, 03:39
chetan2u wrote:
Is $$\frac{|x|}{x} > \frac{|y|}{y}$$, if $$xy\neq{0}$$ ?

(1) $$x<0$$
(2) $$y<0$$

slightly tricky

OE-

Lets analyze the equation first.
$$\frac{|x|}{x} > \frac{|y|}{y}$$

what is the value $$\frac{|x|}{x}...and... \frac{|y|}{y}$$ can take?
Irrespective of NUMERIC value of x and y...$$\frac{|x|}{x}...and... \frac{|y|}{y}$$ will be either 1 or -1...

so two cases..

A) Both x and y are of SAME sign : either + or -...
$$\frac{|x|}{x}$$=$$\frac{|y|}{y}$$....

B) Both x and y are of Different sign :-
If x is + and y is -ive, $$\frac{|x|}{x} > \frac{|y|}{y}$$
If y is + and x is -ive, $$\frac{|x|}{x} < \frac{|y|}{y}$$

so Our ans will be YES, if x is + and y is -ive, Otherwise NO..

lets check the statements-
(1) $$x<0$$
since x<0, our answer for IS $$\frac{|x|}{x} > \frac{|y|}{y}$$ will always be NO..
at the MAX, two sides can be EQUAL
Suff

(2) $$y<0$$..
Two case.
if x<0, ans is NO..
If x>0 ans is YES..
Insuff

ans A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Is |x|/x > |y|/y?  [#permalink]

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20 May 2016, 03:36
5
1
Question: Is |x|/x > |y|/y

Value of |x|/x can be -1 or 1
Similarly, value of |y|/y can be -1 or 1

St1: x < 0 --> x is negative
|x|/x = +ve/-ve = -1
|y|/y can be +1 or -1
Is -1 > 1 ? No
Is -1 > -1 ? No
We get a definite no answer. Sufficient.

St2: y < 0 --> y is negative
|y|/y = +ve/-ve = -1
|x|/x can be -1 or +1
If |x|/x = 1, Is 1 > -1 ? Yes
If |x|/x = -1, Is -1 > -1 ? No
We get two different answers. Not Sufficient.

##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 49300
Re: Is |x|/x > |y|/y?  [#permalink]

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20 May 2016, 03:42
1
chetan2u wrote:
Is $$\frac{|x|}{x} > \frac{|y|}{y}$$?

(1) $$x<0$$
(2) $$y<0$$

slightly tricky
OA in two days

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Good question, kudos!
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Re: Is |x|/x > |y|/y?  [#permalink]

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20 May 2016, 04:20
1
chetan2u wrote:
Is $$\frac{|x|}{x} > \frac{|y|}{y}$$?

(1) $$x<0$$
(2) $$y<0$$

slightly tricky
OA in two days

Is $$\frac{|x|}{x} > \frac{|y|}{y}$$?
Both left hand side and right hand side can have only two values 1 or -1. For a definitive 'yes' answer we need left hand side to be 1 and right hand side to be -1. In other words, we need $$x>0$$ and $$y<0$$. If $$x<0$$ or if $$y>0$$ then left hand side can never be greater than the right side. It can at best be equal to right hand side. Hence, if we know any of these then we will have a definitive 'no' answer.

Statement 1:
$$x<0$$
As mentioned above, this can at best be equal to right hand side (if $$y>0$$) but can never be greater. Hence, we have a definitive no answer.
This statement is sufficient and we can eliminate option B, C and E.

Statement 2:
$$y<0$$.
We have not been given any information about $$x$$. $$x$$ can be both negative and positive.
As mentioned above, if $$x>0$$ and $$y<0$$ then we get a yes answer to the question.
However, if $$x<0$$ and $$y<0$$, then we get a no answer, (as both side will be equal to - 1)
Hence, this statement is insufficient. We can eliminate option D.

chetan2u: Very nice question sir. Would it be better to mention $$xy\neq{0}$$ in the question prompt. Probably I am wrong. I am new to this
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Re: Is |x|/x > |y|/y?  [#permalink]

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20 May 2016, 11:03
chetan2u wrote:
Is $$\frac{|x|}{x} > \frac{|y|}{y}$$, if $$xy\neq{0}$$ ?

(1) $$x<0$$
(2) $$y<0$$

slightly tricky
OA in two days

Information given= xy is not equal to 0

question asked:- $$\frac{|x|}{x} > \frac{|y|}{y}$$

(1) $$x<0$$

That means X is -ve
$$\frac{|x|}{x} is -1(+ve/-ve = -ve) \frac{|y|}{y}$$ can either be 1 ot -1

$$\frac{|x|}{x} > \frac{|y|}{y}$$ will never be possible in both the cases.

(2) $$y<0$$

Y is -ve

$$\frac{|x|}{x} > \frac{|y|}{y}$$ can be possible when X is +ve but not possible when x is -ve.

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26 Dec 2017, 13:55
$$|x|/x > |y|/y$$ ?

will be possible only if x is +ve and y is -ve

so question is x > 0 AND y < 0 ?

Statement 1: x < 0 => sufficient to answer the question, is x > 0 AND y < 0 ? as NO
Statement 2: y < 0 => insufficient to tell about sign of x

Good question chetan2u
Is |x|/x > |y|/y? &nbs [#permalink] 26 Dec 2017, 13:55
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