Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

For statement 2 , the solution says =>(x+2)/x= -2-x. => Multiply both sides by x. => (x+2) = -x(x+2) => x+2= -\(x^2\) - 2x =>\(x^2\) + 3x + 2 = 0. (x+1)(x+2) = 0 x = -1 . x = -2

My question is why cant we cancel out the (x+2) on LHS and RHS instead of multiplying it by x in step. We will get x = -1. So answer should be B instead of C.

Why cant we reduce the equation ? Shall we never do it in GMAT ? Could anyone please explain where equations should be reduced and where they shouldn't be

Re: For all nonzero integers n,n*=(n+2)/n.What is the value of x [#permalink]

Show Tags

26 Oct 2013, 17:51

1

This post received KUDOS

NeetiGupta wrote:

Q. For all non zero integers n,n*=(n+2)/n. What is the value of x ? 1. x* = x. 2. x* = -2-x.

Answer = C.

For statement 2 , the solution says =>(x+2)/x= -2-x. => Multiply both sides by x. => (x+2) = -x(x+2) => x+2= -\(x^2\) - 2x =>\(x^2\) + 3x + 2 = 0. (x+1)(x+2) = 0 x = -1 . x = -2

My question is why cant we cancel out the (x+2) on LHS and RHS instead of multiplying it by x in step. We will get x = -1. So answer should be B instead of C.

Why cant we reduce the equation ? Shall we never do it in GMAT ? Could anyone please explain where equations should be reduced and where they shouldn't be

you can only cancel a factor if it is nonzero. In this case, if you cancel (x+2), you also skip (loose) the root (x+2=0).

Re: For all nonzero integers n,n*=(n+2)/n.What is the value of x [#permalink]

Show Tags

26 Oct 2013, 18:19

5

This post received KUDOS

tuanle wrote:

NeetiGupta wrote:

Q. For all non zero integers n,n*=(n+2)/n. What is the value of x ? 1. x* = x. 2. x* = -2-x.

Answer = C.

For statement 2 , the solution says =>(x+2)/x= -2-x. => Multiply both sides by x. => (x+2) = -x(x+2) => x+2= -\(x^2\) - 2x =>\(x^2\) + 3x + 2 = 0. (x+1)(x+2) = 0 x = -1 . x = -2

My question is why cant we cancel out the (x+2) on LHS and RHS instead of multiplying it by x in step. We will get x = -1. So answer should be B instead of C.

Why cant we reduce the equation ? Shall we never do it in GMAT ? Could anyone please explain where equations should be reduced and where they shouldn't be

you can only cancel a factor if it is nonzero. In this case, if you cancel (x+2), you also skip (loose) the root (x+2=0).

Can you please elaborate "you can only cancel a factor if it is nonzero" Do you mean when we take x=-2. x=2 becomes 0 and hence we cannot cancel it?

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

(1) x* = x. (2) x* = -2-x.

Answer = C.

For statement 2 , the solution says =>(x+2)/x= -2-x. => Multiply both sides by x. => (x+2) = -x(x+2) => x+2= -\(x^2\) - 2x =>\(x^2\) + 3x + 2 = 0. (x+1)(x+2) = 0 x = -1 . x = -2

My question is why cant we cancel out the (x+2) on LHS and RHS instead of multiplying it by x in step. We will get x = -1. So answer should be B instead of C.

Why cant we reduce the equation ? Shall we never do it in GMAT ? Could anyone please explain where equations should be reduced and where they shouldn't be

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

(1) x* = x --> \(\frac{x+2}{x}=x\) --> \(x^2-x-2=0\) --> \(x=-1\) or \(x=2.\) Not sufficient.

(2) x* = -2-x --> \(\frac{x+2}{x}=-2-x\) --> \(x+2=-x(x+2)\) --> \((x+2)(1+x)=0\) --> \(x=-1\) or \(x=-2.\) Not sufficient.

If you divide (reduce) \(x+2=-x(x+2)\) by x+2 you assume, with no ground for it, that x+2 does not equal to zero thus exclude a possible solution (notice that both x=-1 AND x=-2 satisfy the equation).

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

(1)+(2) Common value of x from (1) and (2) is \(x=-1\). Sufficient.

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

Show Tags

17 Dec 2015, 06:16

(1) and (2) are certainly insufficient because they have two solutions each. But how to use (1) and (2) together, simple: (1)=(2) x=-2-x 2x=-2 x=-1 (one solution) sufficient

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

Show Tags

19 Oct 2017, 01:25

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.
_________________