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What is the value of x ?

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What is the value of x ? [#permalink] New post 07 Jun 2012, 22:49
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Question Stats:

53% (02:14) correct 47% (01:00) wrong based on 146 sessions
What is the value of x ?

(1) x^3 = 6x − x^2

(2) 14x = x^3 + 5x^2
[Reveal] Spoiler: OA
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Re: What is the value of x ? [#permalink] New post 07 Jun 2012, 22:57
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macjas wrote:
What is the value of x ?

(1) x^3 = 6x − x^2

(2)14x = x^3 + 5x^2


Statement (1)

x^3 = 6x - x^2

by factoring we have: x (x + 3) ( x - 2) = 0 so x = 0, x = - 3 and x = 2 (ins.)

Statement (2)

14x = x^3 + 5x^2

by factoring we have: x (x + 7) (x - 2) = 0 so x = 0, x = -7 and x = 2 (ins.)

Statement (1) AND (remember in Mathematics "and" means intersection, in layman's term: what is the common in both statement?) Statement (2)

x = 0 as well as x = 2

So still insufficient because we have two values of x

Hope I helped
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Re: What is the value of x ? [#permalink] New post 07 Jun 2012, 23:00
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Hi,

to find the value of x,

using (1)
\(x^3 = 6x-x^2\)
or \(x^3 - 6x + x^2=0\)
or \(x(x^2+x-6)=0\)
or \(x(x+3)(x-2)=0\)
or \(x=-3, 0, 2\), no unique value of x. Insufficient.

using (2)
\(14x = x^3 + 5x^2\)
or \(x^3 + 5x^2-14x=0\)
or \(x(x^2+5x-14)=0\)
or \(x(x+7)(x-2)=0\)
or \(x=-7, 0 , 2\), no unique value of x. Insufficient.

even considering (1) & (2) together,
x=0,2.

Thus, answer is (E)
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Re: What is the value of x ? [#permalink] New post 29 Aug 2012, 03:28
Hi, was just wondering if we could solve it like this:
From 1) x^3 = 6x + x^2
From 2) x^3 = 14x – 5x^2
From 1) and 2), we get 6x – x^2 = 14x – 5x^2
Solving the above, we get, x = 2
Hence, C
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Re: What is the value of x ? [#permalink] New post 27 Feb 2013, 18:10
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reetskaur wrote:
Hi, was just wondering if we could solve it like this:
From 1) x^3 = 6x + x^2
From 2) x^3 = 14x – 5x^2
From 1) and 2), we get 6x – x^2 = 14x – 5x^2
Solving the above, we get, x = 2
Hence, C


Hi,
Even if you solve by the above method you again get two values of x.
4x^2+6x-14x=0
x(4x-8) = 0
x = 0, 2 so Insufficient
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Re: What is the value of x ? [#permalink] New post 27 Feb 2013, 19:25
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As stated in 1)

\(x^3 = 6x - x^2\)

\(x^3 + x^2 -6x = 0\)

\(x (x + 3) ( x - 2) = 0\)

=>\(x = 0, - 3, 2\)

From statement (2)

\(14x = x^3 + 5x^2\)

\(x^3 + 5x^2 - 14x=0\)

\(x (x + 7) (x - 2) = 0\)

=>\(x = 0, -7, 2\)

From Statement (1) AND Statement (2)

x = 0 and 2

So answer is E.
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Re: What is the value of x ? [#permalink] New post 30 Dec 2014, 07:48
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Re: What is the value of x ?   [#permalink] 30 Dec 2014, 07:48
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