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# If x(x-5)(x+2) = 0, is x negative? (1) x^2 - 7x does not

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Manager
Joined: 03 Jul 2008
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If x(x-5)(x+2) = 0, is x negative? (1) x^2 - 7x does not [#permalink]  12 Jul 2008, 06:32
If x(x-5)(x+2) = 0, is x negative?

(1) x^2 - 7x does not eual 0
(2) x^2 - 2x - 15 does not equal 0

Please don't forget to provide a detailed explanation. Thanks
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CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Re: Attention! Calling all maths gurus [#permalink]  12 Jul 2008, 06:42
1
KUDOS
Expert's post
C

x(x-5)(x+2) = 0 --> x is {-2,0,5} [EDIT: typo was corrected]

(1) x^2 - 7x does not eual 0 --> {-2,5} remain --> insufficient
(2) x^2 - 2x - 15 does not equal 0 --> {-2,0} remain --> insufficient
(1)&(2) {-2} remains --> sufficient.
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Manager
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Re: Attention! Calling all maths gurus [#permalink]  12 Jul 2008, 07:31
walker wrote:
C

x(x-5)(x+2) = 0 --> x is {-5,0,2}

(1) x^2 - 7x does not eual 0 --> {-2,5} remain --> insufficient
(2) x^2 - 2x - 15 does not equal 0 --> {-2,0} remain --> insufficient
(1)&(2) {-2} remains --> sufficient.

how did you derive from x(x-5) (x+2) = 0 x is {-5,0,2}
Where did you get the -2 and 5 from in (1)
and where did you get the {-2,0} from in (2) when I factorised I got (x+3) (x-5)

One last question, how do you go about simplifying an equation like

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

Sorry to be a pain but I'm struggling to understand this
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CEO
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Re: Attention! Calling all maths gurus [#permalink]  12 Jul 2008, 09:41
Expert's post
Yeah, It is typo
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Director
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Re: Attention! Calling all maths gurus [#permalink]  12 Jul 2008, 09:56
TheBigCheese wrote:
If x(x-5)(x+2) = 0, is x negative?

(1) x^2 - 7x does not eual 0
(2) x^2 - 2x - 15 does not equal 0

Please don't forget to provide a detailed explanation. Thanks

x(x-5)(x+2) = 0
i.e either x = 0, x = 5 or x = -2

(1)
x^2 - 7x not eq 0
x (x-7) not eq 0
i.e neither x = 0 nor x = 7 not suff. (combining with main statement we know that now x is not eq to 0 but x may be 5 or -2)

(2)
x^2 - 2x - 15 not eq 0
(x-5)(x+3) not eq 0
i.e neither x = 5 nor x = -3 not suff. (combining with main statement we know that now x is not eq to 5 or -3 but x may be 0 or -2)

Combining the two statements together:

x cannot be equal to 0, 7, 5 and -3.

Combining this with original statement. Since x cannot be aeual to 0 and 5 (derived from above two statements). X has to be equal to -2.

Manager
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Re: Attention! Calling all maths gurus [#permalink]  15 Jul 2008, 21:37
would this problem be rated easy, medium or difficult
Director
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Re: Attention! Calling all maths gurus [#permalink]  15 Jul 2008, 21:51
rao_1857 wrote:
TheBigCheese wrote:
If x(x-5)(x+2) = 0, is x negative?

(1) x^2 - 7x does not eual 0
(2) x^2 - 2x - 15 does not equal 0

Please don't forget to provide a detailed explanation. Thanks

x(x-5)(x+2) = 0
i.e either x = 0, x = 5 or x = -2

(1)
x^2 - 7x not eq 0
x (x-7) not eq 0
i.e neither x = 0 nor x = 7 not suff. (combining with main statement we know that now x is not eq to 0 but x may be 5 or -2)

(2)
x^2 - 2x - 15 not eq 0
(x-5)(x+3) not eq 0
i.e neither x = 5 nor x = -3 not suff. (combining with main statement we know that now x is not eq to 5 or -3 but x may be 0 or -2)

Combining the two statements together:

x cannot be equal to 0, 7, 5 and -3.

Combining this with original statement. Since x cannot be aeual to 0 and 5 (derived from above two statements). X has to be equal to -2.

Very Well Explained
Re: Attention! Calling all maths gurus   [#permalink] 15 Jul 2008, 21:51
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# If x(x-5)(x+2) = 0, is x negative? (1) x^2 - 7x does not

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