Is |x|/x |y|/y?

Question

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

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

Self Made 
slightly tricky

Kurtosis · Accepted Answer

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.

Answer: A

chetan2u · Answer

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

Bunuel · Answer

__________________
Good question, kudos!

nalinnair · Answer

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. The correct answer is A. chetan2u : Very nice question sir. Would it be better to mention xy eq{0} in the question prompt. Probably I am wrong. I am new to this

Divyadisha · Answer

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. A is the answer

hellosanthosh2k2 · Answer

|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 Answer (A) Good question chetan2u

CrackverbalGMAT · Answer

|x|/x = 1 when x >0
= -1 when x<0
Similarly
|y|/y = 1 when y >0
= -1 when y<0

Statement 1: x<0
|x|/x = -1

|y|/y could be either 1 or -1
So |x|/x will never be greater than |y|/y

is |x|/x > |y|/y?
Answer is always NO.
So, statement 1 is sufficient to answer the question.

Statement 2: y<0
|y|/y = -1
|x|/x could be either 1 or -1
If |x|/x =1 and 1 > -1 so, |x|/x > |y|/y

If |x|/x =-1, then -1 is not greater than -1
so |x|/x is not greater than |y|/y

is |x|/x > |y|/y?
The answer could be Yes or No, considering both cases

Statement 2 is insufficient

Thanks,
CLIFIN J FRANCIS
GMAT SME

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

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