Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 21 May 2011
Posts: 208

For all non zero integers n, n* = (n+2)/n . What is the
[#permalink]
Show Tags
24 Jul 2011, 12:41
Question Stats:
63% (01:58) correct 37% (02:06) wrong based on 209 sessions
HideShow timer Statistics
For all non – zero integers n, n* = (n+2)/n . What is the value of x ? (1) x* = x (2) x* = – 2 – x
Official Answer and Stats are available only to registered users. Register/ Login.



Retired Moderator
Joined: 20 Dec 2010
Posts: 1836

Re: DS  700 level  n*
[#permalink]
Show Tags
24 Jul 2011, 16:46
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^2x2=0 x^22x+x2=0 (x+1)(x2)=0 x=1, x=2 Not Sufficient. 2) (x+2)/x = 2 x x+2=2xx^2 x^2+3x+2=0 (x+1)(x+2)=0 x=1, x=2 Not Sufficient. Together; x=1 Sufficient. Ans: "C"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 24 Mar 2011
Posts: 372
Location: Texas

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



Intern
Joined: 15 Mar 2010
Posts: 9

Re: DS  700 level  n*
[#permalink]
Show Tags
24 Jul 2011, 20:29
Stmt 1: x* = (x+2)/x = x crossmultiplying:
(x+2) = x*x
solving the quad eqn gives: (x+1)(x2)=0 therefore, x= 1 or x=2 insuff
From stmt 2: (x+2)/ x = x2 cross multiplying:
(x+2)(x+1) =0 gives x=1 or x=2 insuff
Combinig 1 & 2 gives
x= 1 Hence C



Intern
Joined: 08 Jul 2011
Posts: 6

Re: DS  700 level  n*
[#permalink]
Show Tags
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.



Intern
Status: If I play my cards right, I can work this to my advantage
Joined: 18 Jul 2011
Posts: 14
Location: India
Concentration: Operations, Social Entrepreneurship
GMAT Date: 11122011
WE: Information Technology (Telecommunications)

Re: DS  700 level  n*
[#permalink]
Show Tags
26 Jul 2011, 23:37
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



Intern
Joined: 22 Nov 2010
Posts: 8

Re: DS  700 level  n*
[#permalink]
Show Tags
27 Jul 2011, 01:10
One correction: for statement (2) Here (2)we are given that x* = x2 and you were given that x* = (x+2)/x you need to replace the value of x* with x2 in the equation; hence (x2+2)/(x2) = x which becomes x = x^22x. collecting like terms gives x(x+1)=0 which gives the solution of x = 0 or x =1 and the answer becomes C



Intern
Joined: 11 Jul 2011
Posts: 1

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



Current Student
Joined: 21 Aug 2010
Posts: 190

Re: DS  700 level  n*
[#permalink]
Show Tags
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.



Intern
Joined: 06 Apr 2010
Posts: 17

For all non – zero integers [m]n{*}= [fraction]n+2/n[/fraction][/m]
[#permalink]
Show Tags
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



Math Expert
Joined: 02 Sep 2009
Posts: 49858

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



Intern
Joined: 06 Apr 2010
Posts: 17

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



Intern
Joined: 06 Apr 2010
Posts: 17

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



Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: For all non zero integers n, n* = (n+2)/n . What is the
[#permalink]
Show Tags
10 Mar 2016, 09:55
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 > axbx = 0 > x(ab)=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.



Manager
Joined: 31 May 2015
Posts: 93

Re: For all non zero integers n, n* = (n+2)/n . What is the
[#permalink]
Show Tags
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.
_________________
GMAT loosers are born not made !!!



Math Expert
Joined: 02 Sep 2009
Posts: 49858

Re: For all non zero integers n, n* = (n+2)/n . What is the
[#permalink]
Show Tags
14 Apr 2016, 22:38



Manager
Joined: 24 May 2016
Posts: 150

For all non zero integers n, n* = (n+2)/n . What is the
[#permalink]
Show Tags
06 Aug 2016, 12:26
The question stem says that for all nonzero 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 nonzero integer.
So the conclusion in each of the statements would be:
Statement 1: Assuming that x is a nonzero integer, x = 2 or x = 1. Statement 2: Assuming that x is a nonzero integer, x = 2 or x = 1.
Can anyone please correct, extend or clarify this observation?
Thank you.



NonHuman User
Joined: 09 Sep 2013
Posts: 8392

Re: For all non zero integers n, n* = (n+2)/n . What is the
[#permalink]
Show Tags
24 Mar 2018, 06:56
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: For all non zero integers n, n* = (n+2)/n . What is the &nbs
[#permalink]
24 Mar 2018, 06:56






