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

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Re: DS - 700 level - n* [#permalink]
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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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: For all nonzero integers n,n*=(n+2)/n.What is the value of x [#permalink]
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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).
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Re: For all nonzero integers n,n*=(n+2)/n.What is the value of x [#permalink]
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?
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Re: For all non zero integers n, n*=(n+2)/n. What is the value [#permalink]
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Bunuel
I have one query regarding this question.
From statement A, we get the values of x as either -1 or 2.

But if you substitute the original n* equation for these values then the original statement doesn't hold true for the negative value.
n* holds true only for x = 2, so why isn't the answer A in that case?
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Re: For all non zero integers n, n*=(n+2)/n. What is the value [#permalink]
Bunuel
I have one query regarding this question.
From statement A, we get the values of x as either -1 or 2.

But if you substitute the original n* equation for these values then the original statement doesn't hold true for the negative value.
n* holds true only for x = 2, so why isn't the answer A in that case?

Isn't x = -1 a solution of (x + 2)/x = x ?

(-1+2)/(-1) = 1/(-1)= -1.
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Re: For all non zero integers n, n*=(n+2)/n. What is the value [#permalink]
Hi everyone!
Can somebody explain how does in this question "For all non – zero integers n, n* = (n+2)/n . What is the value of x ?", n associate with x?
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Re: For all non zero integers n, n*=(n+2)/n. What is the value [#permalink]
stepanyan wrote:
Hi everyone!
Can somebody explain how does in this question "For all non – zero integers n, n* = (n+2)/n . What is the value of x ?", n associate with x?

The variable "n" is used as an example of a non-zero integer to illustrate how the function denoted by "*" operates. The question states that for any non-zero integer input, the function increases the input by 2 and then divides the result by the input itself. The question then asks to determine the value of some number x. You can check complete solution here: https://gmatclub.com/forum/for-all-non- ... l#p1284216

Hope it helps.
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Re: For all non zero integers n, n*=(n+2)/n. What is the value [#permalink]
Bunuel,
thanks a lot, that was helpful)
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Re: For all non zero integers n, n*=(n+2)/n. What is the value [#permalink]
Hi everyone, one small doubt on association of "x" with "n", we are given that "n" is a non-zero integer. But that is not stated for "x", in the solution are we assuming that "x" is a non-zero integer and that's why the equation of n*=(n+2)/n holds true for x* as well?
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Re: For all non zero integers n, n*=(n+2)/n. What is the value [#permalink]
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Re: For all non zero integers n, n*=(n+2)/n. What is the value [#permalink]
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