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# x/y > 0?

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Intern
Joined: 16 Mar 2017
Posts: 14

Kudos [?]: 9 [0], given: 15

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20 Sep 2017, 05:28
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Difficulty:

55% (hard)

Question Stats:

61% (00:56) correct 39% (01:14) wrong based on 31 sessions

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x/y > 0?

1) x/(x+y) > 0

2) y/(x+y) > 0
[Reveal] Spoiler: OA

Kudos [?]: 9 [0], given: 15

Senior Manager
Joined: 02 Jul 2017
Posts: 252

Kudos [?]: 59 [1], given: 60

Location: India

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20 Sep 2017, 05:46
1
KUDOS
is $$\frac{x}{y}$$> 0?

=> Above equation to be true both x and y should hv same sign => either x and y both +ve or both -ve

1) $$\frac{x}{x+y} > 0$$
=> x and (x+y) both have same sign . both +ve or -ve.
But here we cannot find relation between x and y
eg for below values $$\frac{x}{x+y} > 0$$ is True
x= 10 and y =-5 => $$\frac{x}{y} > 0$$ False

x= 5 and y =5 => $$\frac{x}{y} > 0$$ True
Insufficient

2) $$\frac{y}{x+y} > 0$$
=> Like above equation :
=> y and (x+y) both have same sign . both +ve or -ve.
But here we cannot find relation between x and y
Insufficient

(1)+(2)
=> By combining both equations we get : x , y and (x+y) all three have same sign, +ve or -ve.
=> x and y have same sign
=> $$\frac{x}{y}$$> 0?
Sufficient

Kudos [?]: 59 [1], given: 60

Senior Manager
Joined: 25 Feb 2013
Posts: 417

Kudos [?]: 179 [1], given: 31

Location: India
GPA: 3.82

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20 Sep 2017, 05:52
1
KUDOS
petrified17 wrote:
x/y > 0?

1) x/(x+y) > 0

2) y/(x+y) > 0

Statement 1: the inequality is positive but nothing can be inferred about $$x$$ & $$y$$ individually, they may both be positive or they may both be negative or one may be positive and the other may be negative. Hence Insufficient

Statement 2: Same scenario as Statement 1. Hence Insufficient

Combining 1 & 2: we know LHS of both the inequalities are positive and RHS is $$0$$, so we can divide the inequalities with each other to get

$$\frac{x}{(x+y)}*\frac{(x+y)}{y}>0$$ or $$\frac{x}{y}>0$$. Sufficient

Option C

Kudos [?]: 179 [1], given: 31

SVP
Joined: 05 Jul 2006
Posts: 1750

Kudos [?]: 430 [0], given: 49

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20 Sep 2017, 06:58
We need to know whether x is not 0 and whether x and y have same sign .. both conditions are needed.

From one and two each alone.
We can't deduct that both conditions are a must.

Both together are sufficient

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Kudos [?]: 430 [0], given: 49

Intern
Joined: 19 Sep 2016
Posts: 35

Kudos [?]: 2 [0], given: 3

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20 Sep 2017, 07:28
X/y>0, is possible when both x and y are either positive or both are negative.
Statement 1 - x/(x+y)>0, simplifying we get x*(x+y)>0, which means that x>0 and x+y>0 or x<0 and x+y<0 which means that x/y can be both > and < 0 , hence insufficient.
Statement 2 - y/(x+y)>0, or y*(x+y)>0, which again means that either y and x+y>0 or y and x+y <0 so again insufficient.
Statement 1+2 - clearly states that either x & y both together >0 or both together <0, either ways x/y is >0

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Kudos [?]: 2 [0], given: 3

Re: x/y > 0?   [#permalink] 20 Sep 2017, 07:28
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