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Intern
Joined: 17 Apr 2011
Posts: 4
Followers: 0

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

00:00

Difficulty:

25% (low)

Question Stats:

71% (02:42) correct 28% (01:44) wrong based on 38 sessions
I found this question in a practice test and am not able to comprehend the solution to the problem. The question is as follows:

Is x + y > 0 ?
(I) x² - y² > 1
(II) x/y + 1 > 0

I marked the answer as B using the following approach,
x/y + 1 > 0
x/y > -1
x > -y
x + y > 0

But the correct answer this E. Can someone please explain this? Thanks!
[Reveal] Spoiler: OA
CEO
Joined: 17 Nov 2007
Posts: 3600
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 316

Kudos [?]: 1564 [1] , given: 354

1
KUDOS
Expert's post
Welcome to GMAT Club!

Here is a 10-sec solution:

x^2, y^2, x/y - are insensitive to changing simultaneously signs of x and y but x+y reverses its sign. So, it's E
In other words, let's say, if x=-5; y=-1 satisfies both conditions, x=5; y=1 will satisfy them too, but the answer will be different.
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CEO
Joined: 17 Nov 2007
Posts: 3600
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 316

Kudos [?]: 1564 [0], given: 354

Expert's post
gujralvikas wrote:
x/y + 1 > 0
x/y > -1
x > -y
x + y > 0

x/y > -1 ---> x > -y (only if y>=0)! So you forgot to consider x < -y for y<0
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SVP
Joined: 16 Nov 2010
Posts: 1698
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 28

Kudos [?]: 261 [0], given: 36

Let x = 2, y = 1

and x = -2, y = -1

then both (1) and (2) are correct, but x+y > 0 or x+y < 0.

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4049
Location: Pune, India
Followers: 864

Kudos [?]: 3631 [1] , given: 144

1
KUDOS
Expert's post
gujralvikas wrote:
I found this question in a practice test and am not able to comprehend the solution to the problem. The question is as follows:

Is x + y > 0 ?
(I) x² - y² > 1
(II) x/y + 1 > 0

I marked the answer as B using the following approach,
x/y + 1 > 0
x/y > -1
x > -y
x + y > 0

But the correct answer this E. Can someone please explain this? Thanks!

I am not solving the question since walker has already given you a very impressive logical solution and subhashghosh has shown the solution using 'plugging in numbers'.
But, let me add something here, "You multiply/divide an inequality by a number only if you know whether the number is negative or positive."
If the number is positive, fine. Just go ahead and do what you do in case of equations.
If the number is negative, there is no problem either but remember, you have to flip the inequality sign.

e.g.
Given: x < y
Multiply by 5: 5x < 5y
Multiply by -5: -5x > -5y
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VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1368
Followers: 9

Kudos [?]: 115 [0], given: 10

a+b

x = +|- 3 and y = +|- 2 gives different values for x+y > 0. Not sufficient.

E it is.
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