idontknowwhy94 wrote:

Is x<0?

1) \(x^{3} + x^{2}\) + x + 2 = 0

2) \(x^{2}\)-x-2 < 0

Keep the Kudos coming in and let the questions come out

Responding to a pm:

**Quote:**

For statement 1 it is clear that x >= 0 but when I tested -ve values I didn't find any which can satisfy the equation. Though I knew that x < 0, I continuously tried to find some -ve value that satisfied the equation. But it was a waste of time to find the value. How can I crack these type of traps on GMAT or it is my lack of understanding of concepts.

In stmnt 1, note that the point is that x cannot be positive or 0. So it has to be negative (since it has to be real).

If x is positive, all terms are positive and their sum cannot be 0.

If x is 0, you get 2 = 0 which is not valid.

So x has to be negative. No need to look for the actual value. It will not be an integer.

\(x^{3} + x^{2}+ x + 2 = 0\)

If you plug in x = -1, you get 1 = 0

If you plug in x = -2, you get -4 = 0

So somewhere in between -1 to -2, x will take a value such that you will get 0 = 0

_________________

Karishma

Private Tutor for GMAT

Contact: bansal.karishma@gmail.com