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If x(x - 5)(x + 2) = 0, is x negative?

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vaivish1723
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If x(x - 5)(x + 2) = 0, is x negative? [#permalink] New post   17 Jan 2010, 10:43
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If x(x - 5)(x + 2) = 0, is x negative?

(1) x^2 – 7x ≠ 0
(2) x^2 –2x –15 ≠ 0
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C
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If x(x - 5)(x + 2) = 0, is x negative? [#permalink] New post   17 Jan 2010, 13:24
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If x(x - 5)(x + 2) = 0, is x negative?

\(x(x - 5)(x + 2) = 0\) --> \(x=0\) or \(x=5\) or \(x=-2\). Question is \(x<0\) or is \(x=-2\)?

(1) x^2 – 7x ≠ 0 --> \(x(x-7)\neq{0}\)--> \(x\neq{0}\) and \(x\neq{7}\), so \(x\) can be 5 or -2 (from the stem as \(x=0\) is out). Not sufficient.

(2) x^2 –2x –15 ≠ 0 --> \((x+3)(x-5)\neq{0}\) --> \(x\neq{-3}\) and \(x\neq{5}\), so \(x\) can be 0 or -2 (from the stem as \(x=5\) is out). Not sufficient.

(1)+(2) As \(x=0\) and \(x=5\) are out, only value left is \(x=-2\), so \(x\) is negative. Sufficient.

Answer: C.
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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink] New post   04 Jul 2013, 08:23
For the given equation to be equal to 0 x must either equal 0, 5 or -2.

Statement 1: Tells us that x cannot equal 0 or 7. But it could equal 5 or -2. Not sufficient
Statement 2: Tells us that x cannot equal 5 or -3. But it could equal -2 or 0.

Taken together x cannot equal 0 or 5. Therefore, x must equal -2. Answer: C
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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink] New post   30 Dec 2013, 22:20
vaivish1723 wrote:
If x(x - 5)(x + 2) = 0, is x negative?

(1) x^2 – 7x ≠ 0
(2) x^2 –2x –15 ≠ 0


We definitely need to bold or make larger the not equals symbol in the question. From a distance it looks like an equals symbol.
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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink] New post   18 Oct 2014, 13:49
Either X = 0 OR X = 5 OR X = -2 . Is X = -2?

1. X cannot be 0 or 7 ==> X can be 5 or -2. NS
2. X cannot be 5 or -3 ==> X can be 0 or -2. NS

1&2. X cannot be 0 or 5 so X = -2, Sufficient.

ANSWER: C

vaivish1723 wrote:
If x(x - 5)(x + 2) = 0, is x negative?

(1) x^2 – 7x ≠ 0
(2) x^2 –2x –15 ≠ 0
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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink] New post   09 Sep 2017, 08:38
I did silly mistake in factorising - (2) "x^2 –2x –15 ≠ 0" - marked B
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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink] New post   23 Nov 2020, 19:43
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vaivish1723 wrote:
If x(x - 5)(x + 2) = 0, is x negative?

(1) x^2 – 7x ≠ 0
(2) x^2 –2x –15 ≠ 0


(1) \(x(x-7) ≠ 0\)

x ≠ 0, 7

INSUFFICIENT.

(2) \(x^2-2x-15≠0\)
x ≠ 5, -3

INSUFFICIENT.

(1&2) We're told \(x(x - 5)(x + 2) = 0\)
x ≠ 5, 0. Therefore x must be -2. SUFFICIENT.

Answer is C.
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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink] New post   28 Oct 2023, 09:54
Hello from the GMAT Club BumpBot!

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).

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Re: If x(x - 5)(x + 2) = 0, is x negative? [#permalink]
28 Oct 2023, 09:54
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