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

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Senior Manager
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If x(x - 5)(x + 2) = 0, is x negative? [#permalink]

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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
[Reveal] Spoiler: OA
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Kudos [?]: 79367 [2] , given: 10016

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17 Jan 2010, 13:24
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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

OA is
[Reveal] Spoiler:
c

Pl explain.

$$x(x - 5)(x + 2) = 0$$ --> $$x=0$$ 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.

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

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03 Jul 2013, 01:17
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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

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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]

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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]

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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.

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]

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15 Jan 2016, 07:05
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] 15 Jan 2016, 07:05
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