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# What is the value of x ?

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Senior Manager
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Joined: 09 May 2012
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What is the value of x ? [#permalink]

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07 Jun 2012, 23:49
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Difficulty:

55% (hard)

Question Stats:

53% (01:12) correct 47% (01:01) wrong based on 157 sessions

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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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Manager
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Re: What is the value of x ? [#permalink]

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07 Jun 2012, 23:57
1
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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]

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08 Jun 2012, 00:00
2
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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.

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Re: What is the value of x ? [#permalink]

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29 Aug 2012, 04:28
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]

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27 Feb 2013, 19:10
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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]

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27 Feb 2013, 20:25
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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

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Re: What is the value of x ? [#permalink]

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30 Dec 2014, 08:48
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Re: What is the value of x ?   [#permalink] 30 Dec 2014, 08:48
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