If x and y are non-zero integers. Is

Question

GMATBusters’ Quant Quiz Question -10

If x and y are non-zero integers. Is  \frac{(x+y)}{(x-y)} >0?
1) x > y
2) |x| > |y|

Raxit85 · Answer

If x and y are non-zero integers. Is (x+y)/(x−y)>0?

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

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

(2) |x| > |y|
√(x^2 ) > . √(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

Imo. B

akadiyan · Answer

Given: X and Y are Non-Zero Integers

We know that X and Y are Integers. X and Y is not equal to 0.

We do not know X and Y is either Positive / Negative ir Even / Odd.

1) X > Y

Both x and y positives - Lets consider x=3, y= 2 , (x+y)/(x-y) > 0 
Both x and y negatives - lets consider x=-2, y=-3 , (x+y)/(x-y) < 0

We get 2 different answers, so option 1 is not sufficient.

2) |x| > |y|

Both x and y positives , lets consider x=2,y=1 , (x+y)/(x-y) > 0
Both x and y negatives, lets consider x=-3 , y=-2, (x+y)/(x-y) > 0

In both the choices we get (x+y) / (x-y) > 0

Option B alone is sufficient.

Ans:   B

yashikaaggarwal · Answer

OA is A.
Statement one is alone sufficient.
Statement 1: (x+y)/(x-y)>0
X>Y (given)
Let X = 2 and Y=1
2+1/2-1=3
Which is greater than zero. (Sufficient)
Statement 2: |x|>|y|
Case 1: x>-y
Case 2: x>y
Case 3: -x>-y
Case 4: -x>y (not possible)
If we put X=2 and Y=1 in above cases in the given solution. It's not confirmed that the answer will always be greater than zero.(insufficient)
So Statement A is sufficient alone.
OA is A

Posted from my mobile device

Kinshook · Answer

If x and y are non-zero integers.  Is \frac{(x+y)}{(x−y)}>0?

1) x > y
x-y>0
If y>0;  \frac{(x+y)}{(x−y)}>0 
But if y<0;  \frac{(x+y)}{(x−y)} may not be>0 
NOT SUFFICIENT

2) |x| > |y| 
If x = 3; y = -2 ;  \frac{(x+y)}{(x−y)}= 1/5>0 
But If x = -3; y = -2 ;  \frac{(x+y)}{(x−y)}= (-5/-1)>0 
We see that if |x|>|y| then signs of (x+y) & (x-y) are determined by signs of x and are either both +ve or both -ve
SUFFICIENT

IMO B

ashwini2k6jha · Answer

Answer : B
Statement:1
x>y
3>2,x+y/x-y=5/1>0,yes
-2>-3,x+y/x-y=-5<0,No
Not sufficient
Statement 2
IxI >IyI,then x+y/x-y>0 for x=3,y=2 and x=-3,y=-2.Also for x=-3,y=2
Hence x+y/x-y>0 for all input
Sufficient

abannore · Answer

Statement 1: x>y
If both x & y are positive, say x= 8, y = 3
\(\frac{x+y}{x-y}\) > 0

If both x and y are negative, say x = -2, y = -5
\(\frac{x+y}{x-y}\)
\(\frac{-7}{3}\) < 0

Insufficient

Statement 2: |x| > |y|
\(x^2\) > \(y^2\)
\(x^2 - y^2\) > 0
(x+y)(x-y) > 0
x<-y or x>y
x+y<0 or x-y>0

case 1: x+y<0
x=-2, y=-3: \(\frac{x+y}{x-y}\) = \(\frac{-5}{1}\) < 0
x=-4, y=-1 : \(\frac{x+y}{x-y}\) = \(\frac{-5}{-3}\) > 0

case 2: x-y>0
x=5, y=2: \(\frac{x+y}{x-y}\) = \(\frac{7}{3}\) > 0
x=-5, y=-7: \(\frac{x+y}{x-y}\) = \(\frac{-12}{2}\) < 0

Insufficient

Statement 1 & 2: Since x>y,
x=-2, y=-3: \(\frac{x+y}{x-y}\) = \(\frac{-5}{1}\) < 0
x=5, y=2: \(\frac{x+y}{x-y}\) = \(\frac{7}{3}\) > 0
Insufficient

Answer: E

ArunSharma12 · Answer

statement 1: x > y
case A: both x & y are negative
 \frac{x+y}{x-y}<0 ; y is higher magnitude negative value.

case B: both x & y are positive

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

not sufficient

statement 2: |x| > |y|
this tells us that magnitude of x is greater than magnitude of y.

case A: both x & y are negative

\frac{x+y}{x-y}>0 ; x is higher magnitude negative value.

case B: both x & y are positive

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

case C: x is negative and y is positive

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

sufficient

Ans: B

TheNightKing · Answer

Statement 1:

1) x > y

Case 1: -2>-3 Gives us -5 and that's not greater than 0
Case 2: 3>2 Gives us 5 and that's greater than 0

Not Sufficient.

Statement 2: |x| > |y|

This ensures that case 1 is not possible from above. So we are left with case 2

Also checking: x=-3 y =-2 works. We have -5/(-3+2) = 5 greater than 0.

Sufficient.

Answer B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x and y are non-zero integers. Is

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If x and y are non-zero integers. Is

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards