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# Is it true that x > 0?

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Manager
Joined: 14 Oct 2014
Posts: 66
Location: United States
GMAT 1: 500 Q36 V23
Is it true that x > 0? [#permalink]

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30 Nov 2014, 16:40
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55% (hard)

Question Stats:

52% (00:43) correct 48% (00:55) wrong based on 148 sessions

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Is it true that x > 0?

(1) x^2 = 2x
(2) x^3 = 3x

[Reveal] Spoiler:
The GMAC explanation for the statement (2) states, that for the x^3=3x, values for x are 0 and 3. It sounds incorrect to me.
[Reveal] Spoiler: OA
Senior Manager
Joined: 13 Jun 2013
Posts: 277
Re: Is it true that x > 0? [#permalink]

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01 Dec 2014, 02:07
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viktorija wrote:
Is it true that x>0?

(1) x^2=2x
(2) x^3=3x

The GMAC explanation for the statement (2) states, that for the x^3=3x, values for x are 0 and 3. It sounds incorrect to me.

st.1
$$x^2=2x$$
$$x^2-2x=0$$
$$x(x-2)=0$$

$$x=0$$ or $$x=2$$ . For x=0 answer to the question is no and for x=2, answer is yes. hence st.1 alone is not sufficient

st.2
$$x^3=3x$$
$$x(x^2-3)=0$$
$$x(x-\sqrt{3})(x+\sqrt{3})=0$$
$$x=0$$, $$x=\sqrt{3}$$ or $$x= -\sqrt{3}$$
clearly both yes and no answer to the original question are possible hence not sufficient

st.1 + st.2

the only common solution for both of these equation is x=0, which results in the answer to the original question as no.

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Re: Is it true that x > 0? [#permalink]

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12 Feb 2018, 17:14
viktorija wrote:
Is it true that x > 0?

(1) x^2 = 2x
(2) x^3 = 3x

x^2 = 2x

We can solve the equation as follows:

x^2 - 2x = 0

x(x - 2) = 0

x = 0 or x = 2

We see that if x = 0, then x is not greater than 0. However, if x = 2, then x is greater than 0. Statement one alone is not sufficient.

Statement Two Alone:

x^3 = 3x

We can solve the equation as follows:

x^3 - 3x = 0

x(x^2 - 3) = 0

x = 0 or x^2 = 3
x = 0 or x = √3 or x = -√3

We see that if x = 0 or -√3, then x is not greater than 0. However, if x = √3, then x is greater than 0. Statement two alone is not sufficient.

Statements One and Two Together:

Using both statements, we see that x can only be 0. Thus, x is not greater than 0. Both statements together are sufficient.

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Re: Is it true that x > 0?   [#permalink] 12 Feb 2018, 17:14
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# Is it true that x > 0?

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