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Is integer x negative?

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Is integer x negative? [#permalink]

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New post 27 Apr 2011, 16:05
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Question Stats:

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Is integer x negative?

(1) \(x^2 = -5x\)
(2) \(|x| = -x\)
[Reveal] Spoiler: OA

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Re: Is integer x negative? [#permalink]

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New post 27 Apr 2011, 16:59
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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.

Combining both;
X can be 0 or -ve.

Not Sufficient.

Ans: "E"
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Re: Is integer x negative? [#permalink]

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New post 27 Apr 2011, 17:16
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fluke wrote:

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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Re: Is integer x negative? [#permalink]

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New post 27 Apr 2011, 17:17
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.

Combining both;
X can be 0 or -ve.

Not Sufficient.

Ans: "E"

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Re: Is integer x negative? [#permalink]

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New post 27 Apr 2011, 19:24
Yalephd wrote:
Is integer x negative

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


x<0?

(1) \(X^2 = -5x\)
\(X^2 + 5X = 0\)
\((X)(X + 5) = 0\)
Solutions: x=0 OR x = -5
INSUFFICIENT

(2) \(|X| = -X\)
\(|X| + X = 0\)
Solutions: x=0 OR x<0
INSUFFICIENT

Therefore, E

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Re: Is integer x negative? [#permalink]

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New post 27 Apr 2011, 20:19
(1)

x^2 = -5x

so x can be 0 or -5

(2)

|X| = -X

X can be 0 or any -ve Integer


(1) and two are insufficient too,

Answer - E
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Re: Is integer x negative? [#permalink]

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New post 28 Apr 2011, 01:22
a gives x=0 or -5
b gives x-0 or <0

a+b gives essentially the same interpretation for values of x.

Hence E.
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Re: Is integer x negative? [#permalink]

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New post 30 Apr 2011, 12:50
i agree with fluke's explanation above

1. Not sufficient

x can be 0 or -ve

2. Not sufficient
x can be 0 or - ve

together still not sufficient as x can be 0 or <0

Answer is E .

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Re: Is integer x negative? [#permalink]

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Re: Is integer x negative? [#permalink]

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New post 12 Oct 2017, 18:15
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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Re: Is integer x negative?   [#permalink] 12 Oct 2017, 18:15
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