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Q: Is x<0? 1. \(X^2=-5x\). It looks like a trick to use block "X" and small "x". The expression is equivalent to \(X^2=-5z\). "x"(small x) may be 0 or -ve. Not Sufficient.

2. \(|X|=-X\) This expression will hold good for any \(X \le 0\) X can be 0 or -ve. Not Sufficient.

1. \(X^2=-5x\). It looks like a trick to use block "X" and small "x".

I'd bet that was just a typo - I'm sure the 'X' is supposed to be the same as the 'x'. The real GMAT would never mix capital and small letters in the same equation, at any rate. If that's the case, then from Statement 1 we know:

x^2 + 5x = 0 x(x + 5) = 0

and since one of our factors must equal zero, either x=0 or x=-5. So x might be negative, and might not be negative, and the statement is not sufficient. Similarly Statement 2 is true for x=0 and for any negative number, so the answer is E.
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Sorry about that. Didn't mean the have different cases of X. I'll revise the question:

Is integer \(X\) negative

(1) \(X^2 = -5X\) (2) \(|X| = -X\)

I'll leave the original as is so that your answer below makes sense for other viewers.

fluke wrote:

Yalephd wrote:

Is integer x negative

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

Sol:

Q: Is x<0? 1. \(X^2=-5x\). It looks like a trick to use block "X" and small "x". The expression is equivalent to \(X^2=-5z\). "x"(small x) may be 0 or -ve. Not Sufficient.

2. \(|X|=-X\) This expression will hold good for any \(X \le 0\) X can be 0 or -ve. Not Sufficient.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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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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