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# Is x + y > 0 ?

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Intern
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Is x + y > 0 ? [#permalink]  26 Dec 2010, 07:31
00:00

Difficulty:

65% (hard)

Question Stats:

42% (02:21) correct 58% (01:02) wrong based on 53 sessions
Is x + y > 0 ?

(1) x^2 - y^2 > 1
(2) x/y + 1 > 0
[Reveal] Spoiler: OA
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Re: Inequalities [#permalink]  26 Dec 2010, 21:55
1
KUDOS
Expert's post
surendar26 wrote:
Is x + y > 0 ?
(I) x² - y² > 1
(II) x/y + 1 > 0

(I) x² - y² > 1
(x + y)(x - y) is positive. So either both are positive or both are negative. Also, absolute value of x is greater than absolute value of y.
e.g. x = 3, y = 2, then (x + y) = 5 and (x+y)(x - y) = 5
x = -4, y = -2, then (x + y) = -6 and (x + y)(x - y) = 12
(x + y) can be positive or negative. Not sufficient.

(II) x/y + 1 > 0
(x+y)/y > 0
So either both are positive or both are negative.
e.g. y positive. y = 4, x = 3, then (x+y) = 7 and (x + y)/y = 7/4
y negative. y = -4, x = 3, then (x+y) = -1 and (x + y)/y = (-1)/(-4) = 1/4
So x + y can be positive or negative. Not sufficient.

Taking both together,
(x+y), (x -y) and y, all have the same signs. The same examples as shown for statement I above satisfy this condition.
e.g. y positive. x = 3, y = 2, then (x + y) = 5, (x - y) = 1
y negative. x = -4, y = -2, then (x + y) = -6, (x - y) = -2
(x + y) can be positive or negative. Not sufficient.

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Joined: 30 Aug 2010
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Location: Bangalore, India
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Kudos [?]: 117 [0], given: 27

Re: Inequalities [#permalink]  31 Jan 2011, 04:46
surendar26 wrote:
Is x + y > 0 ?
(I) x² - y² > 1
(II) x/y + 1 > 0

Let me solve it the way GMAT expects us to do.

qtn: Is X+Y positive?

stmnt1:
$$x^2 - y^2 > 1$$
==> $$(x+1)(x-y) > 1$$
==> $$(x+y)(x-y)$$ shud surely be > 0 as it is > 1
(> 1, instead of > 0, is given just to make the statement more indirect/confusing)
==> $$(x+y)(x-y)$$ is positive
==> $$(x+y)$$ and $$(x-y)$$ both, at the same time, are positive or nagative...not suff.

stmnt2
$$\frac{x}{y} + 1$$ > 0
==> $$(x+y)/y$$ > 0
==> $$(x+y)/y$$ is positve
again $$(x+y)$$ and $$y$$both, at the same time, are positive or nagative...not suff.

stmnts1 and 2 together: $$X+Y$$ cab be positive or negative...NOT suff.

Regards,
Murali.
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Re: Check this one out - Algebra [#permalink]  04 Feb 2011, 11:27
Expert's post
Merging similar topics.

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

Simple logic would probably be the best way to deal with this question (without much calculation, algebra and number plugging).

Is x + y > 0 ?

Question asks whether the sum of $$x$$ and $$y$$ is positive.

(1) x² - y² > 1 --> if $$x$$ is some big enough positive number and $$y$$ is some small enough positive number (for example $$x=2$$ and $$y=1$$) then the answer will obviously be YES as the sum of two positive values is positive BUT if you consider the same values but with the minus sign ($$x=-2$$ and $$y=-1$$) then again the answer will obviously be NO as the sum of two negative values is negative. Not sufficient.

(2) x/y + 1 > 0 --> exact same approach for this statement: if both $$x$$ and $$y$$ are positive (which satisfies the given statement as x/y+1=positive/positive+positive) then the answer will be YES BUT if both $$x$$ and $$y$$ are negative (which also satisfies the given statement as x/y+1=negative/negative+positive=positive+positive) then the answer will be NO. Not sufficient.

(1)+(2) Two positive values and two negative values from (1), also satisfy (2), so we still have two answers. Not sufficient.

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Kudos [?]: 60 [0], given: 66

Re: Check this one out - Algebra [#permalink]  05 Feb 2011, 09:46
Bunuel wrote:
Merging similar topics.

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

Simple logic would probably be the best way to deal with this question (without much calculation, algebra and number plugging).

Is x + y > 0 ?

Question asks whether the sum of $$x$$ and $$y$$ is positive.

(1) x² - y² > 1 --> if $$x$$ is some big enough positive number and $$y$$ is some small enough positive number (for example $$x=2$$ and $$y=1$$) then the answer will obviously be YES as the sum of two positive values is positive BUT if you consider the same values but with the minus sign ($$x=-2$$ and $$y=-1$$) then again the answer will obviously be NO as the sum of two negative values is negative. Not sufficient.

(2) x/y + 1 > 0 --> exact same approach for this statement: if both $$x$$ and $$y$$ are positive (which satisfies the given statement as x/y+1=positive/positive+positive) then the answer will be YES BUT if both $$x$$ and $$y$$ are negative (which also satisfies the given statement as x/y+1=negative/negative+positive=positive+positive) then the answer will be NO. Not sufficient.

(1)+(2) Two positive values and two negative values from (1), also satisfy (2), so we still have two answers. Not sufficient.

Yeah I chose E too. I wanted to see how you would approach this q. I took the statements apart to find the q simpler to solve... Thank you Bunuel!
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Is x + y > 0 ? [#permalink]  28 May 2011, 05:51
1
This post was
BOOKMARKED
Is x + y > 0 ?

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

[Reveal] Spoiler:
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!

Last edited by Bunuel on 10 Jun 2014, 13:03, edited 1 time in total.
Renamed the topic and edited the question.
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Kudos [?]: 2140 [2] , given: 359

2
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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Kudos [?]: 2140 [0], given: 359

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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Joined: 16 Nov 2010
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Kudos [?]: 342 [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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2
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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a+b

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

E it is.
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Re: Is x + y > 0 ? [#permalink]  23 Feb 2014, 03:41
Expert's post
Bumping for review and further discussion.
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