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x and y are consecutive positive integers and: \left{

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Senior Manager
Senior Manager
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Joined: 05 Oct 2008
Posts: 273
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Kudos [?]: 57 [0], given: 22

x and y are consecutive positive integers and: \left{ [#permalink] New post 25 Oct 2008, 20:16
x and y are consecutive positive integers and:
\left{ \begin{eqnarray*} x &>& y\\ x^2 - 1 &>& y^2 - 4y + x - 1\\ \end{eqnarray*}

Which of the following represents all the possible values of y ?


* y \ge 0
* y > 0
* y > 1
* y > 7
* y > 8
1 KUDOS received
VP
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Joined: 30 Jun 2008
Posts: 1048
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Kudos [?]: 291 [1] , given: 1

Re: Math Question [#permalink] New post 26 Oct 2008, 06:32
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study wrote:
x and y are consecutive positive integers and:
\left{ \begin{eqnarray*} x &>& y\\ x^2 - 1 &>& y^2 - 4y + x - 1\\ \end{eqnarray*}

Which of the following represents all the possible values of y ?


* y \ge 0
* y > 0
* y > 1
* y > 7
* y > 8

here we do not need to plug in numbers

Ok.... now we know x>0 and y>0 and x,y are consecutive

we know x>y ..... this means x=y+1 ( x,y consecutive)

x² -1 > y²-4y+x-1
(y+1)² -1 > y²-4y+ (y+1) -1 -------- [ here i have substituted x=y+1]
y²+2y+1 -1 > y²-4y +y+1-1
y²+2y > y²-4y +y
y²+2y > y²-3y
2y > -3y
5y >0
y>0


SO B

Hope this helps
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Senior Manager
Senior Manager
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Joined: 05 Oct 2008
Posts: 273
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Kudos [?]: 57 [0], given: 22

Re: Math Question [#permalink] New post 25 Oct 2008, 20:50
Mostly, everyone who posts questions on this website has an answer to the question, unless specified otherwise. Please provide an explanation to the answer as a mere Answer Choice in the reply is not of much help.

Thanks!!
Director
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Posts: 840
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Kudos [?]: 29 [0], given: 0

Re: Math Question [#permalink] New post 25 Oct 2008, 21:41
study wrote:
Mostly, everyone who posts questions on this website has an answer to the question, unless specified otherwise. Please provide an explanation to the answer as a mere Answer Choice in the reply is not of much help.

Thanks!!


x and y are positive and consecutive integers. I just plugged in values that satisfied those conditions. lowest value for Y is 1
Manager
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Re: Math Question [#permalink] New post 26 Oct 2008, 05:42
study wrote:
x and y are consecutive positive integers and:
\left{ \begin{eqnarray*} x &>& y\\ x^2 - 1 &>& y^2 - 4y + x - 1\\ \end{eqnarray*}

Which of the following represents all the possible values of y ?


* y \ge 0
* y > 0
* y > 1
* y > 7
* y > 8


No creative solution from me I'm sorry, I'm also going for B.

Explanation:
By definition of condition 1, x>y, therefore x=y+1 (since they are consecutive)

I then just plugged in values, starting from y=1, x=2; y=1 seems to work, therefore y>0 is my answer. Note I start from y=1, as y=0 is not possible due to question conditions (y is positive integer)


Seems a bit too straight forward though, what did I miss?
Manager
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Kudos [?]: 47 [0], given: 0

Re: Math Question [#permalink] New post 26 Oct 2008, 07:33
amitdgr wrote:
here we do not need to plug in numbers

Ok.... now we know x>0 and y>0 and x,y are consecutive

we know x>y ..... this means x=y+1 ( x,y consecutive)

x² -1 > y²-4y+x-1
(y+1)² -1 > y²-4y+ (y+1) -1 -------- [ here i have substituted x=y+1]
y²+2y+1 -1 > y²-4y +y+1-1
y²+2y > y²-4y +y
y²+2y > y²-3y
2y > -3y
5y >0
y>0


SO B

Hope this helps


Thanks, that solution seems more logical.
Manager
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Joined: 15 Oct 2008
Posts: 54
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Kudos [?]: 2 [0], given: 0

Re: Math Question [#permalink] New post 28 Oct 2008, 05:28
WOW !! thank you amitdgr..
Senior Manager
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Re: Math Question [#permalink] New post 29 Oct 2008, 07:54
Amitgdr very good explanation - kudos given. thanks.
Re: Math Question   [#permalink] 29 Oct 2008, 07:54
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