Folks, I'm confused about the solution to this Q

Is x=1
1) x^3 + x^2 = 2x
2) x not equal to -2

2 is not the answer and on looking at 1, the right answer is factoring it down. However, can't I simply substitute x=1 in the equation? If I do, both sides equal up to 2 and the final answer can be A. I kind of think this approach is wrong but can't figure out why

Thank you

I was able to answer it myself by substituting -2 and since -2 works as well, 1 cannot be the only answer

Hence the final answer is E

Hi samcr22:
Let's break this problem down:

1) Our question is "is x=1"? So this is a yes/no question.

2) Start with statement #2 because it is easier. Statement #2 tells us that x is NOT equal to 2. Does it answer the question whether x=1? No, it doesn't. x could be 1, or it could be another number. x just cannot be 2.

Since we started with statement #2, your grid should be BD/ACE. Cross off BD since statement #2 is insufficient.

3) Let's evaluate statement #1, which says x^3 + x^2 = 2x.
Let's subtract 2x from both sides, so we have x^3 + x^2 -2x = 0.

Now let's factor out an x. That gives me x(x^2 + x - 2). Now let's factor our quadratic. I get x(x+2)(x-1)=0.

I know that any of these terms could be equal to zero to get the result of 0. So I need to set x=0, x+2 =0, and x-1=0. Thus x could be 0, -2, or 1. This statement does not tell me if x = 1. Not sufficient. Cross off A.

4) Can we combine the two? From Statement #1 I know x is 0, -2, or 1. Statement #2 tells me x is NOT -2. That leaves me with x is 0 or 1. Again, not sufficient to determine whether x=1. My answer is E.

_________________
Jamie Nelson
ManhattanGMAT Instructor

Question :

Is X = 1 ?

Statement 1 :
It is intuitive that x = 0 is also a solution to this equation (apart from 1), hence we cant decide if x = 1
So Not Sufficient

Statement 2:
Because x is not equal to -2 , it could be any value other than -2, not necessarily 1 :)

Combining 1 and 2,
the problem , as in statement 1 still remains, we still can't choose between 0 and 1

So E

Thank you atul. Looks like you and I agree in our explanations. :-)

_________________
Jamie Nelson
ManhattanGMAT Instructor

Sorry guys, why cant we approach in the following way?

x^3+x^2=2x
=> x^2+x=2
=> x(x+1)=2
=> x is either -2 or 1.
Then using the other piece of data (x<>-2) we can draw the conclusion that x=1

Hence C is the answer.

Hi Ankeet, by dividing by x on both sides, you got rid of one of the roots of equation, that is 0.
Since the highest power of the variable in this equation is 3, it is bound to have 3 roots(unless some of them are same).

In my opinion refrain from simplifying by factoring out and cancelling a term unless you have taken into account its role in the equation. (here the cancelled term x had a possible value of 0)

Thanks Atul. That clarifies.

Nice teamwork, folks!