If |x| = |y|, is x/y = -1 (1) x 0

Question

If |x| = |y|, is  \frac{x}{y} = -1 ?

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

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • We need to find if  \frac{x}{y} = -1 
• We have, | x| = |y|, this means there can be two cases:
 o Case 1: If both x and y have the same signs i.e. both are either negative or both are positive, in that case x= y
  For example, x = 2 and y = 2, here |x| = |y|
 And in this case,  \frac{x}{y} = 1  
o Case 2: If both x and y have opposite signs i.e. one of them is negative and other one is positive, in that case x = -y
  For example, x = 2 and y = -2, here |x| = |y|
 However, in this case  \frac{x}{y} = -1    
So basically, we need to find whether x and y have opposite signs or not.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  x< 0
 • According to this statement: x is negative
• However, this statement says nothing about the sign of y. 
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  y > 0
 • According to this statement: y is positive.
• However, this statement says nothing about the sign of x. 
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.

Step 3: Analyse Statements by combining. 
 • From statement 1: x is negative.
• From statement 2: y is positive.
• On combining both statements, we get,
 o x and y are of opposite signs.
  Therefore,  \frac{x}{y} = -1    
Thus, the correct answer is  Option C.

stne · Answer

Hi  DaniGmat77 ,

We know |x| = |y| so Let x=1 y= 1 or x=-1 y= -1 or x=1 y =-1 or x= -1 y=1

(1) x < 0

If x=-1 and y=1 then  \frac{x}{y}  = -1 and ans. is yes
If x=-1 and y=-1 then  \frac{x}{y} =1 and ans. is no
NOT SUFF.

(2) y > 0

If x=-1 and y=1 then  \frac{x}{y}  = -1 and ans. is yes
If x= 1 and y=1 then  \frac{x}{y} =1 and ans. is no
NOT SUFF.

1+2

We know x=-1 and y=1 hence  \frac{x}{y}  =-1 and ans. is yes.
SUFF.

Ans-C

Hope it's clear.

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If |x| = |y|, is x/y = -1 (1) x < 0 (2) y > 0

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