If x ≠ y and x and y are non-zero integers, is (x+y)/(x−y)0?

Question

If x ≠ y and x and y are non-zero integers, is (x+y)/(x−y) > 0?

(1) x > y
(2) |x| > |y|

raarun · Answer

The question basically asks are both x+y and x-y positive or negative?

(1) x > y
(2) |x| > |y|

Stmnt 1:
x-y> 0 => x-y is positive
says nothing about x+y which can either be positive or negative
Insufficient

Stmnt 2
 \sqrt{x^2}>\sqrt{y^2} 
x^2-y^2 > 0
(x+y)(x-y) > 0
so both x+y and x-y can be positive or 
both x+y and x-y can be negative
This means that x+y /x-y will always be positive and greater than 0
Sufficient

Ans B

adityagupta2102 · Answer

(x + y)/(x - y) = (x + y)(x - y) / (x - y) (x - y) = (x^2 -y^2)/(x - y)^2 
we know x is not equal to y , so (x - y)^2 is always > 0
Therefore x^2 - y^2 > 0
So , x^2 > y^2
Hence, |x| > |y|.

Ans- B

akshanka1 · Answer

\frac{x+y}{x-y} > 0

Multiplying numerator and denominator by x-y, we get,

x^2-y^2 >0  i.e.  x^2>y^2  and hence |x| > |y|

1. x>y is clearly not sufficient
2|x|>|y| , this what our deduced expressions ask for!

Hence, B

Izzyjolly · Answer

(1) x > y

If x=2, y=1 then (x+y)/(x−y) = 3/1 = 3 > 0 --> Yes.
If x=1, y=-1 then (x+y)/(x−y) = 0/2 = 0 --> No.
 --> Not sufficient.

(2) |x| > |y| -->  x^2 > y^2  -->  x^2-y^2 > 0  -->  (x+y)(x-y) > 0  -->  (x+y) / (x−y)   > 0  --> Yes --> Sufficient.

Answer B.

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If x ≠ y and x and y are non-zero integers, is (x+y)/(x−y)>0?

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