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bschool83
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For all non zero integers n, n*=(n+2)/n. What is the value 24 Jul 2011, 12:41
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C
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66% (01:59) correct 34% (02:04) wrong based on 621 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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C
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Bunuel
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For all non zero integers n, n*=(n+2)/n. What is the value 27 Oct 2013, 06:50
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NeetiGupta
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
Show more

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.

Answer: C.

Similar question to practice: https://gmatclub.com/forum/for-all-inte ... 55982.html

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

(1) x * = x

(2) x * = – 2 – x
Show more

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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For all non zero integers n, n*=(n+2)/n. What is the value 26 Jul 2011, 13:17
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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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For all non zero integers n, n*=(n+2)/n. What is the value 26 Jul 2011, 23:37
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elementbrdr
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.
Show more

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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For all non zero integers n, n*=(n+2)/n. What is the value 26 Oct 2013, 18:51
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NeetiGupta
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
Show more
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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For all non zero integers n, n*=(n+2)/n. What is the value 26 Oct 2013, 19:19
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tuanle
NeetiGupta
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).
Show more


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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For all non zero integers n, n*=(n+2)/n. What is the value 31 Jul 2022, 02:48
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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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For all non zero integers n, n*=(n+2)/n. What is the value 31 Jul 2022, 04:53
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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?
Show more

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

(-1+2)/(-1) = 1/(-1)= -1.
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For all non zero integers n, n*=(n+2)/n. What is the value 07 Mar 2023, 13:08
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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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For all non zero integers n, n*=(n+2)/n. What is the value 07 Mar 2023, 13:40
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stepanyan
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?
Show more

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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For all non zero integers n, n*=(n+2)/n. What is the value 08 Mar 2023, 11:04
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Bunuel,
thanks a lot, that was helpful)
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For all non zero integers n, n*=(n+2)/n. What is the value 26 Apr 2023, 13:12
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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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For all non zero integers n, n*=(n+2)/n. What is the value 15 Jun 2025, 22:43
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