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

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Intern
Joined: 22 Jul 2013
Posts: 12
GMAT 1: 650 Q48 V31
For all non zero integers n, n*=(n+2)/n. What is the value  [#permalink]

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Updated on: 27 Oct 2013, 06:40
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Difficulty:

55% (hard)

Question Stats:

64% (01:27) correct 36% (01:35) wrong based on 301 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.

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.

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

Originally posted by NeetiGupta on 26 Oct 2013, 18:20.
Last edited by Bunuel on 27 Oct 2013, 06:40, edited 2 times in total.
Edited the question.
Intern
Joined: 05 Oct 2013
Posts: 21
Re: For all nonzero integers n,n*=(n+2)/n.What is the value of x  [#permalink]

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26 Oct 2013, 18:51
1
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.

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.

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).
Intern
Joined: 22 Jul 2013
Posts: 12
GMAT 1: 650 Q48 V31
Re: For all nonzero integers n,n*=(n+2)/n.What is the value of x  [#permalink]

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26 Oct 2013, 19:19
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.

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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 47983
Re: For all non zero integers n, n*=(n+2)/n. What is the value  [#permalink]

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27 Oct 2013, 06:50
2
1
NeetiGupta wrote:
For all non zero integers n, n*=(n+2)/n. What is the value of x ?

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

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.

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.

Similar question to practice: for-all-integers-n-n-n-n-1-what-is-the-value-of-x-155982.html

Hope this helps.
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Joined: 11 Dec 2012
Posts: 31
Re: For all non zero integers n, n*=(n+2)/n. What is the value  [#permalink]

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17 Dec 2015, 07:16
(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
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Re: For all non zero integers n, n*=(n+2)/n. What is the value  [#permalink]

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19 Oct 2017, 02:25
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Re: For all non zero integers n, n*=(n+2)/n. What is the value &nbs [#permalink] 19 Oct 2017, 02:25
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