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For all non zero integers n, n* = (n+2)/n . What is the

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New post 24 Jul 2011, 12:41
5
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:58) correct 37% (02:06) wrong based on 209 sessions

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For all non – zero integers n, n* = (n+2)/n . What is the value of x ?

(1) x* = x

(2) x* = – 2 – x
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Re: DS - 700 level - n*  [#permalink]

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New post 24 Jul 2011, 16:46
1
bschool83 wrote:
For all non – zero integers n , n* = (n+2)/n . What is the value of x ?

(1) x * = x

(2) x * = – 2 – x


1)
(x+2)/x=x
x+2=x^2
x^2-x-2=0
x^2-2x+x-2=0
(x+1)(x-2)=0
x=-1, x=2
Not Sufficient.

2)
(x+2)/x = -2 -x
x+2=-2x-x^2
x^2+3x+2=0
(x+1)(x+2)=0
x=-1, x=-2
Not Sufficient.

Together;
x=-1
Sufficient.

Ans: "C"
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Re: DS - 700 level - n*  [#permalink]

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New post 24 Jul 2011, 19:42
yes agree with fluke's solution, it is C.
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Re: DS - 700 level - n*  [#permalink]

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New post 24 Jul 2011, 20:29
Stmt 1: x* = (x+2)/x = x
crossmultiplying:

(x+2) = x*x

solving the quad eqn gives:
(x+1)(x-2)=0 therefore, x= -1 or x=2 insuff

From stmt 2: (x+2)/ x = -x-2
cross multiplying:

(x+2)(x+1) =0 gives x=-1 or x=-2 insuff

Combinig 1 & 2 gives

x= -1 Hence C
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Re: DS - 700 level - n*  [#permalink]

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New post 26 Jul 2011, 13:17
I don't have any issues with the mechanics of solving this question. I can factor and derive the roots for each equation pretty handily. However, I don't understand conceptually what the roots {2, -2} are. Are they correct values for x in statements (1) and (2) respectively but not for the entire system of equations. And when a question asks for a value, must there always be only a single value?

Thanks, and I'm happy to attempt to clarify my question if it's confusing.
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Re: DS - 700 level - n*  [#permalink]

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New post 26 Jul 2011, 23:37
1
elementbrdr wrote:
I don't have any issues with the mechanics of solving this question. I can factor and derive the roots for each equation pretty handily. However, I don't understand conceptually what the roots {2, -2} are. Are they correct values for x in statements (1) and (2) respectively but not for the entire system of equations. And when a question asks for a value, must there always be only a single value?

Thanks, and I'm happy to attempt to clarify my question if it's confusing.


yes DS questions always ask for a definite (one) value only from what i've solved till now from OG / Kaplan ...
any solution in this case quadratic, having 2 roots; is not sufficient

that is the reason the definate solution is by combining the two solutions of (1) and (2) option
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Re: DS - 700 level - n*  [#permalink]

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New post 27 Jul 2011, 01:10
One correction: for statement (2)
Here (2)we are given that x* = -x-2 and you were given that x* = (x+2)/x you need to replace the value of x* with -x-2 in the equation; hence (-x-2+2)/(-x-2) = x which becomes -x = -x^2-2x. collecting like terms gives x(x+1)=0 which gives the solution of x = 0 or x =-1 and the answer becomes C
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Re: DS - 700 level - n*  [#permalink]

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New post 04 Aug 2011, 22:26
For all non – zero integers n , n* = (n+2)/n . What is the value of x ?

(1) x * = x

(2) x * = – 2 – x

I think answer is B. Correct me if i am wrong.

from statement 2

x*= (x+2)/ x= -2-x
=> (x+2)/ x= - (x+2)
=> 1/x= -1
=> x= -1
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Re: DS - 700 level - n*  [#permalink]

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New post 05 Aug 2011, 04:26
The answer is C :
1. Gives the values of x = -1, -2 which is insufficient
2. Gives the values of x = -1, 2 which is again insufficient

Combining both we get -1 as the value for x. So C is the answer.
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For all non – zero integers [m]n{*}= [fraction]n+2/n[/fraction][/m]  [#permalink]

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New post 09 Mar 2016, 11:33
For all non – zero integers \(n{*}= \frac{n+2}{n}\) . What is the value of x ?
(1) x * = x
(2) x * = – 2 – x
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Re: For all non zero integers n, n* = (n+2)/n . What is the  [#permalink]

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New post 09 Mar 2016, 11:36
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Re: For all non zero integers n, n* = (n+2)/n . What is the  [#permalink]

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New post 09 Mar 2016, 13:10
Bunuel wrote:
ninayeyen wrote:
For all non – zero integers \(n{*}= \frac{n+2}{n}\) . What is the value of x ?
(1) x * = x
(2) x * = – 2 – x


Merging topics. Please refer to the discussion above.



Okay thank you Bunuel!
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Re: For all non zero integers n, n* = (n+2)/n . What is the  [#permalink]

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New post 10 Mar 2016, 09:32
Bunuel wrote:
ninayeyen wrote:
For all non – zero integers \(n{*}= \frac{n+2}{n}\) . What is the value of x ?
(1) x * = x
(2) x * = – 2 – x


Merging topics. Please refer to the discussion above.


Hello Bunuel, I understand the solution to this question and how the answer is C. However, could you take a look at sbhuyan86 solution in the thread and explain why his logic is wrong? It has me a little confused there becAUSE I could also solve it this way and get B. Thanks
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Re: For all non zero integers n, n* = (n+2)/n . What is the  [#permalink]

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New post 10 Mar 2016, 09:55
1
ninayeyen wrote:
Bunuel wrote:
ninayeyen wrote:
For all non – zero integers \(n{*}= \frac{n+2}{n}\) . What is the value of x ?
(1) x * = x
(2) x * = – 2 – x


Merging topics. Please refer to the discussion above.


Hello Bunuel, I understand the solution to this question and how the answer is C. However, could you take a look at sbhuyan86 solution in the thread and explain why his logic is wrong? It has me a little confused there becAUSE I could also solve it this way and get B. Thanks


It is a very basic but an important consideration that you are missing.

If I ask you if ax=bx and I do not tell you anything else, can you say a=b ? If you say yes or no unambiguously, then your answer is NOT correct. This is because if you do go ahead and cancel x from both sides, you are inherently assuming that x \(\neq\)0 but did I tell you that ? No. So you could not have cancelled x from both sides.

ax=bx ---> ax-bx = 0 --> x(a-b)=0 ---> either x=0 or a=b .

Coming back to the main question, if you do cancel x+2 from both sides, you are assuming that x \(\neq\) -2, which is not true as the question does NOT mention anything like that.

This is the reason B is NOT sufficient. Do not even cancel variables, until you are either given such information or can deduce such with absolute certainty.

Hope this helps.
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Re: For all non zero integers n, n* = (n+2)/n . What is the  [#permalink]

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New post 14 Apr 2016, 15:36
Would the following be a logical approach.....

We know :

(1) x* = x

(2) x* = – 2 – x

Then x = -2 -x
2x = - 2
x = - 1 which satisfies all above.
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Re: For all non zero integers n, n* = (n+2)/n . What is the  [#permalink]

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New post 14 Apr 2016, 22:38
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New post 06 Aug 2016, 12:26
The question stem says that for all non-zero integers n, n* = (n+2) / n.

But if n = 0 or n = 1.1, what is the value of x? On such case, we cannot derive anything about the value of x.

Therefore, when we go to each of the statements, we have to assume that x has to be a non-zero integer.

So the conclusion in each of the statements would be:

Statement 1: Assuming that x is a non-zero integer, x = 2 or x = -1.
Statement 2: Assuming that x is a non-zero integer, x = -2 or x = -1.

Can anyone please correct, extend or clarify this observation?

Thank you.
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Re: For all non zero integers n, n* = (n+2)/n . What is the  [#permalink]

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