Is x + y 0 (1) x/y -1 (2) y -x

Question

Is  x +y > 0

(1)  \frac{x}{y} > -1

(2)  y > -x

chetan2u · Answer

Three cases 1) Both x and y >0....YES 2) Both x and y <0...NO 3) One>0 and other <0....Will depend on the value of x and y. (I) \frac{x}{y}>-1 If \frac{x}{y}>0 ...YES If -1<\frac{x}{y}<0 ...NO (II) y>-x Add x to both the sides of inequality.. x+y>x-x.....x+y>0 B

Russ19 · Answer

BrentGMATPrepNow , could you please resolve the problem above?

BrentGMATPrepNow · Answer

Target question :    Is  x +y > 0?

Statement 1 :  \frac{x}{y} > -1   
There are several values of x and y that satisfy statement 1. Here are two: 
 Case a : x = 1 and y = 1. In this case, x + y = 1 + 1 = 2. So, the answer to the target question is  YES, x+y is greater than 0 
 Case b : x = -1 and y = -1. In this case, x + y = (-1) + (-1) = -2. So, the answer to the target question is  NO, x+y is not greater than 0 
Since we can’t answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 :  y > -x  
Add  x  to both sides of the inequality to get:  y + x > 0 
So, the answer to the target question is  YES, x+y is greater than 0 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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hiranmay · Answer

Is x +y > 0 (1) \frac{x}{y} > -1 --> insuff: \frac{x}{y} > -1 => \frac{xy}{y^2} > -1 => y>-y^2 => y(x+y)>0, now if y >0, then x+y > 0, then the answer is YES, but if y < 0, then x+y < 0, then the answer is NO (2) y > -x --> suff: y > -x => x+y > 0, so the answer is YES Answer: B

rcgard · Answer

Is x+y>0
x
+
y
>
0

(1) xy>−1
x
y
>
−
1

(2) y>−x
y
>
−
x

Solution:
Is x+y>0?
1) \(\frac{(x)}{(y)}>-1\)
\(\frac{(x)}{(y)}+1>0\) ?
\(\frac{(x+y)}{(y)}>0\) ?
If y<0 then x+y<0, if y>0 then x+y>0
Insufficient

2) y>-x
x+y>0
Sufficient

Answer Choice B

Is x + y > 0 (1) x/y > -1 (2) y > -x

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