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# Does x^2-y^2 = x+y (1) x and y are consecutive integers (2)

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VP
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Does x^2-y^2 = x+y (1) x and y are consecutive integers (2) [#permalink]

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21 Aug 2008, 02:29
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Does $$x^2-y^2 = x+y$$

(1) x and y are consecutive integers

(2) x= 1+y

Guys, I got this question from one of the CAT tests from the princeton review. To be honest, I got pissed of for getting this problem wrong because I chose D, but the OA is B?? I'm getting confused with something here. Whenever a question or a statement says that x and y are consecutive integers, doesn't that ALWAYS mean that x is smaller than y? The OE says that we don't know whether x or y is bigger, but I honestly think that this is such a BS thing to say. I've always worked with problems that would say x and y are consecutive integers and it is always understood that y is bigger than x. what do you guys think?
Senior Manager
Joined: 16 Jul 2008
Posts: 285
Re: DS: I don't agree with the OA [#permalink]

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21 Aug 2008, 04:35
I also arrived at B. Why should you assume that y is the greater integer?
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VP
Joined: 21 Jul 2006
Posts: 1491
Re: DS: I don't agree with the OA [#permalink]

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21 Aug 2008, 04:58
well, because have you tried several questions from the official guide? there are numerous other questions that would say x and y are consecutive integers, but then you never would need to wonder whether the consecutive integers are descending or ascending...this problem makes this distinction. Anything consecutive always assumes numbers running from left to right. As long as the GMAT is not written in arabic, we shouldn't assume that the integers could also run from right to left. lol...

There are other problems that I made a mistake in because I assumed that consecutive integers could mean descending, but then I got penalized for that as well. so where can we draw the line here?? I even remember posting a question that I got it wrong sometime ago. I wish I could find that question again, but I've posted way too many questions that it will be hard to find it again. My mistake in that last post was that I assumed that consecutive integers could also mean descending, but I was wrong....now in this question, not considering the descending side made me get it wrong....WTF??

Last edited by tarek99 on 21 Aug 2008, 05:06, edited 1 time in total.
Senior Manager
Joined: 16 Jul 2008
Posts: 285
Re: DS: I don't agree with the OA [#permalink]

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21 Aug 2008, 05:05
I am studying from OG, but cannot remember any examples right now. Can you post an OG question with consecutive intergers?
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VP
Joined: 21 Jul 2006
Posts: 1491
Re: DS: I don't agree with the OA [#permalink]

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21 Aug 2008, 05:08
Nerdboy wrote:
I am studying from OG, but cannot remember any examples right now. Can you post an OG question with consecutive intergers?

I'll try to look it up and post it for you. I'll also try to look up for that other post that I made sometime ago. This is really frustrating....sometimes descending consecutive integers should be considered, and then sometimes doing so is wrong...I really hate contradictions.
SVP
Joined: 07 Nov 2007
Posts: 1761
Location: New York
Re: DS: I don't agree with the OA [#permalink]

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21 Aug 2008, 07:33
tarek99 wrote:
Does $$x^2-y^2 = x+y$$

(1) x and y are consecutive integers

(2) x= 1+y

Guys, I got this question from one of the CAT tests from the princeton review. To be honest, I got pissed of for getting this problem wrong because I chose D, but the OA is B?? I'm getting confused with something here. Whenever a question or a statement says that x and y are consecutive integers, doesn't that ALWAYS mean that x is smaller than y? The OE says that we don't know whether x or y is bigger, but I honestly think that this is such a BS thing to say. I've always worked with problems that would say x and y are consecutive integers and it is always understood that y is bigger than x. what do you guys think?

Hi tarek,
you can't assume that y is bigger than x.

x and y are consecutive integers --> y>x or x>y
x and y are consecutive integers in the ascending order --> y>x
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Manager
Joined: 15 Jul 2008
Posts: 205
Re: DS: I don't agree with the OA [#permalink]

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21 Aug 2008, 07:39
tarek99 wrote:
well, because have you tried several questions from the official guide? there are numerous other questions that would say x and y are consecutive integers, but then you never would need to wonder whether the consecutive integers are descending or ascending...this problem makes this distinction. Anything consecutive always assumes numbers running from left to right. As long as the GMAT is not written in arabic, we shouldn't assume that the integers could also run from right to left. lol...

There are other problems that I made a mistake in because I assumed that consecutive integers could mean descending, but then I got penalized for that as well. so where can we draw the line here?? I even remember posting a question that I got it wrong sometime ago. I wish I could find that question again, but I've posted way too many questions that it will be hard to find it again. My mistake in that last post was that I assumed that consecutive integers could also mean descending, but I was wrong....now in this question, not considering the descending side made me get it wrong....WTF??

Relax dude
Even if i agree with your logic and take y>x, it will still be insufficient. What if both x and y are negative and y>x ? In this case, statement 1 will be insufficient.

eg. x=-3 y=-2
x^2 - y^2 = 5
x+y = -5

So u c, the answer is B.
VP
Joined: 21 Jul 2006
Posts: 1491
Re: DS: I don't agree with the OA [#permalink]

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21 Aug 2008, 09:21
bhushangiri wrote:
tarek99 wrote:
well, because have you tried several questions from the official guide? there are numerous other questions that would say x and y are consecutive integers, but then you never would need to wonder whether the consecutive integers are descending or ascending...this problem makes this distinction. Anything consecutive always assumes numbers running from left to right. As long as the GMAT is not written in arabic, we shouldn't assume that the integers could also run from right to left. lol...

There are other problems that I made a mistake in because I assumed that consecutive integers could mean descending, but then I got penalized for that as well. so where can we draw the line here?? I even remember posting a question that I got it wrong sometime ago. I wish I could find that question again, but I've posted way too many questions that it will be hard to find it again. My mistake in that last post was that I assumed that consecutive integers could also mean descending, but I was wrong....now in this question, not considering the descending side made me get it wrong....WTF??

Relax dude
Even if i agree with your logic and take y>x, it will still be insufficient. What if both x and y are negative and y>x ? In this case, statement 1 will be insufficient.

eg. x=-3 y=-2
x^2 - y^2 = 5
x+y = -5

So u c, the answer is B.

yeah, REALLY good point. So we don't consider the two possibilities of going up or down. We should ONLY consider it in an increasing order from left to right. The only issue to look into is whether all the numbers are positive or negative. This is it! because I do remember VERY WELL for getting a certain problem wrong for simply considering both up and down when dealing with consecutive integers. So we should ONLY consider whether the consecutive integers are positive or negative! thanks a lot!
Senior Manager
Joined: 16 Jul 2008
Posts: 285
Re: DS: I don't agree with the OA [#permalink]

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22 Aug 2008, 00:08
Actually, it doesn't work with y>x no matter if they are positive or negative. It works with x>y, again no matter if positive or negative.

x=-2; y=-3
x+y = (x+y)(x-y) = -5

x=3; y=2
x+y = (x+y)(x-y) = 5

x=-3; y=-2 - does not work as shown

x=2; y=3
x+y = 5
(x+y)(x-y) = -5
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VP
Joined: 21 Jul 2006
Posts: 1491
Re: DS: I don't agree with the OA [#permalink]

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22 Aug 2008, 12:57
bhushangiri wrote:
tarek99 wrote:
well, because have you tried several questions from the official guide? there are numerous other questions that would say x and y are consecutive integers, but then you never would need to wonder whether the consecutive integers are descending or ascending...this problem makes this distinction. Anything consecutive always assumes numbers running from left to right. As long as the GMAT is not written in arabic, we shouldn't assume that the integers could also run from right to left. lol...

There are other problems that I made a mistake in because I assumed that consecutive integers could mean descending, but then I got penalized for that as well. so where can we draw the line here?? I even remember posting a question that I got it wrong sometime ago. I wish I could find that question again, but I've posted way too many questions that it will be hard to find it again. My mistake in that last post was that I assumed that consecutive integers could also mean descending, but I was wrong....now in this question, not considering the descending side made me get it wrong....WTF??

Relax dude
Even if i agree with your logic and take y>x, it will still be insufficient. What if both x and y are negative and y>x ? In this case, statement 1 will be insufficient.

eg. x=-3 y=-2
x^2 - y^2 = 5
x+y = -5

So u c, the answer is B.

actually, I just realized your error here. -3 - (-2) is NOT equal to -5, but rather -1, so it still doesn't solve the problem because even if x=2 and y=3, then we will still have -1 : 2-3= -1 ....so we're still back to the same issue now...

you see, the equation $$x^2-y^2=x+y$$ becomes:
$$(x+y) (x-y) = x+y$$
therefore: $$x-y = 1$$

this is why I chose D because statement one gave me -1 in either way....hmm...i'm 100% sure that I came across other questions that penalizes the test taker for considering the consecutive integers in descending order. i just don't know what to trust anymore! lol...help please

Last edited by tarek99 on 22 Aug 2008, 13:06, edited 2 times in total.
Manager
Joined: 15 Jul 2008
Posts: 205
Re: DS: I don't agree with the OA [#permalink]

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22 Aug 2008, 12:59
tarek99 wrote:
bhushangiri wrote:
tarek99 wrote:
well, because have you tried several questions from the official guide? there are numerous other questions that would say x and y are consecutive integers, but then you never would need to wonder whether the consecutive integers are descending or ascending...this problem makes this distinction. Anything consecutive always assumes numbers running from left to right. As long as the GMAT is not written in arabic, we shouldn't assume that the integers could also run from right to left. lol...

There are other problems that I made a mistake in because I assumed that consecutive integers could mean descending, but then I got penalized for that as well. so where can we draw the line here?? I even remember posting a question that I got it wrong sometime ago. I wish I could find that question again, but I've posted way too many questions that it will be hard to find it again. My mistake in that last post was that I assumed that consecutive integers could also mean descending, but I was wrong....now in this question, not considering the descending side made me get it wrong....WTF??

Relax dude
Even if i agree with your logic and take y>x, it will still be insufficient. What if both x and y are negative and y>x ? In this case, statement 1 will be insufficient.

eg. x=-3 y=-2
x^2 - y^2 = 5
x+y = -5

So u c, the answer is B.

actually, I just realized your error here. -3 + (-2) is NOT equal to -5, but rather -1, so it still doesn't solve the issue....so we're back to the same issue now...

I made no error there buddy. Check ur algebra.
-3 + (-2) is -5. but -3 - (-2) is -1

Last edited by bhushangiri on 22 Aug 2008, 13:02, edited 3 times in total.
VP
Joined: 21 Jul 2006
Posts: 1491
Re: DS: I don't agree with the OA [#permalink]

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22 Aug 2008, 13:09
sorry guys, I made a typo in my last message. please take a look at it again.
thanks
Manager
Joined: 15 Jul 2008
Posts: 205
Re: DS: I don't agree with the OA [#permalink]

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22 Aug 2008, 13:28
tarek99 wrote:
sorry guys, I made a typo in my last message. please take a look at it again.
thanks

okies ... i see ur point. and my bad.. regardless of whether x and y are negative or positive, as long as they are consecutive such that y>x, x-y will always be -1 and x^2 - y^2 will be negative of x+y.

It does boil down to how you construe consecutive integers x and y.
Re: DS: I don't agree with the OA   [#permalink] 22 Aug 2008, 13:28
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