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# Is it true that x > 0?

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Manager
Joined: 14 Oct 2014
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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:

48% (01:11) correct 52% (01:14) wrong based on 289 sessions

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

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01 Dec 2014, 02:07
2
1
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.

thus answer should be C
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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]

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24 Jul 2018, 21:35
JeffTargetTestPrep wrote:
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.

why can't x2 = 2x be re-written as x multiplied by x= 2 multiplied by x and then cancel x with x an thus the answer is x=2 and thus A is sufficient?
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Re: Is it true that x > 0?  [#permalink]

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24 Jul 2018, 21:49
2
Shbm wrote:
JeffTargetTestPrep wrote:
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.

why can't x2 = 2x be re-written as x multiplied by x= 2 multiplied by x and then cancel x with x an thus the answer is x=2 and thus A is sufficient?

You cannot reduce x^2 = 2x by x because x can be 0 and we cannot divide by 0. By doing so you loose a root, namely x = 0.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.

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

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25 Jul 2018, 00:07
2
Hi,

This is one of the popular traps in GMAT, that is, Cancelling of common variables on both sides.

Never fall for such a trap, i.e., do not cancel common variables on both sides of an equation unless it is already mentioned in the question as variables(unknowns) not equal to zero.

Statement I is insufficient:

x^2 = 2x

x^2 – 2x = 0

x(x-2) = 0

x and x-2 are two numbers, for the product to be zero not necessary that both of them have to be zero.

Either x = 0 or x-2 = 0

i.e.,

x=0 or x =2

If x = 0, then answer to the question is NO.

If x = 2, then answer to the question is YES.

Two answers are there, so not sufficient.

Here, easily most of the students end up cancelling “x” on both sides and say x =2, which is wrong to do, as x can be equal to 0.

Statement II is insufficient:

x^3 = 3x

Similar to statement I,

x^3 – 3x = 0

x(x^2-3) = 0

So, either x = 0 or x^2 -3 = 0

i.e., x = 0 or x = +/- (root 3).

Again we will have yes or no answer to the question.

So not sufficient.

Both statements together,

x=0 is the only value which satisfy both statements.

So answer has to be C(Together Sufficient).

While practicing learn from your mistakes.

Hope this helps.
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Re: Is it true that x > 0?  [#permalink]

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24 Mar 2019, 07:44
Top Contributor
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.

Target question: Is it true that x > 0?

Statement 1: x² = 2x
Rewrite as: x² - 2x = 0
Factor: x(x - 2) = 0
So, EITHER x = 0 OR x = 2
Let's examine each possible case
Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0
Case b: If x = 2, then the answer to the target question is YES, it is true that x > 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x³ = 3x
Rewrite as: x³ - 3x = 0
Factor: x(x² - 3) = 0
Factor again: x(x - √3)(x + √3) = 0
So, x = 0, OR x = √3 OR x = -√3
Let's examine each possible case
Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0
Case b: If x = √3, then the answer to the target question is YES, it is true that x > 0
Case c: If x = -√3,, then the answer to the target question is NO, it is not true that x > 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = 0 OR x = 2
Statement 2 tells us that x = 0, OR x = √3 OR x = -√3
The only x-value that satisfies BOTH statements is x = 0
So, the answer to the target question is NO, it is not true that x > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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

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25 Mar 2019, 08:50
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.

#1
x(x-2)=0
x=0,+2
insufficient
#2
x(x^2-3)=0
x=0 and x=+/-√3
insufficient
from 1 & 2
x=0
sufficeint
IMO C
Re: Is it true that x > 0?   [#permalink] 25 Mar 2019, 08:50
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