Yalephd wrote:

Is integer x negative?

(1) \(x^2 = -5x\)

(2) \(|x| = -x\)

Statement One Alone:

x^2 = -5x

Simplifying the above equation, we have:

x^2 + 5x = 0

x(x + 5) = 0

x = 0 or x = -5

Thus, we do not know whether x is negative, since x could be 0. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

|x| = -x

The equation is true if and only if x is nonpositive. For example, if x = 0, then |0| = -0 since both sides can be simplified to be 0. If x = -1, then |-1| = -(-1) since both sides can be simplified to be 1. Since x can be either 0 or some negative number, statement two alone is not sufficient to answer the equation.

Statements One and Two Together:

From statement one, x could be 0 or -5. From statement two, x could be 0 or any negative number. Thus, we still don’t have enough information to determine if x is negative (since there is a possibility that x = 0).

Answer: E

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