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# Is x + y > 0 ?

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

45% (medium)

Question Stats:

37% (02:19) correct 63% (01:06) wrong based on 46 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
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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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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Manager Joined: 30 Aug 2010 Posts: 93 Location: Bangalore, India Followers: 3 Kudos [?]: 94 [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 yboth, at the same time, are positive or nagative...not suff. stmnts1 and 2 together: X+Y cab be positive or negative...NOT suff. Answer "E". Regards, Murali. Kudos? Math Expert Joined: 02 Sep 2009 Posts: 18851 Followers: 3274 Kudos [?]: 22872 [0], given: 2651 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. Answer: E. _________________ Senior Manager Joined: 30 Nov 2010 Posts: 264 Schools: UC Berkley, UCLA Followers: 1 Kudos [?]: 54 [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. Answer: E. 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! _________________ Thank you for your kudoses Everyone!!! "It always seems impossible until its done." -Nelson Mandela Intern Joined: 17 Apr 2011 Posts: 5 Followers: 0 Kudos [?]: 0 [0], given: 0 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. CEO Joined: 17 Nov 2007 Posts: 3605 Concentration: Entrepreneurship, Other Schools: Chicago (Booth) - Class of 2011 GMAT 1: 750 Q50 V40 Followers: 351 Kudos [?]: 1697 [2] , given: 354 Re: Please help me with this question [#permalink] 28 May 2011, 06:11 2 This post received 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. _________________ HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame CEO Joined: 17 Nov 2007 Posts: 3605 Concentration: Entrepreneurship, Other Schools: Chicago (Booth) - Class of 2011 GMAT 1: 750 Q50 V40 Followers: 351 Kudos [?]: 1697 [0], given: 354 Re: Please help me with this question [#permalink] 28 May 2011, 06:14 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 _________________ HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame SVP Joined: 16 Nov 2010 Posts: 1692 Location: United States (IN) Concentration: Strategy, Technology Followers: 30 Kudos [?]: 276 [0], given: 36 Re: Please help me with this question [#permalink] 29 May 2011, 08:40 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. Answer - E _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) Get the best GMAT Prep Resources with GMAT Club Premium Membership Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4598 Location: Pune, India Followers: 1043 Kudos [?]: 4559 [2] , given: 162 Re: Please help me with this question [#permalink] 29 May 2011, 14:15 2 This post received 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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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
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Bumping for review and further discussion.
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