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Is it true that x>0?

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Source: — Data Sufficiency |
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by aj5105 » Sun May 17, 2009 9:24 am
Statement 1:

x^2 = 2x

x = 2

Sufficient

Statement 2:

x^3 = 3x

x * x^2 = 3x

x^2 = 3

x = + root3

Insufficient.

(A)
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by Jose Ferreira » Sun May 17, 2009 9:24 am
Great question!

Statement 1:
x can equal 0 or 2 and satisfy this equation, so it must be insufficient.
(0)^2=2(0)
(2)^2=2(2)

Statement 2:
x can equal 0 or sqrt3 or -sqrt3, so it is also insufficient.
(0)^3=3(0)
(sqrt3)^3=(sqrt3)^3

Put the statements together, and we see that the only number that satisfies both equations is 0. So, the answer to the original question is "No," but you cannot confuse an answer of "No" with a lack of sufficiency.

The Answer is C
Last edited by Jose Ferreira on Wed May 20, 2009 10:24 am, edited 3 times in total.
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by aj5105 » Sun May 17, 2009 9:29 am
Jose, could you please correct my mistake?

Thanks,
AJ
Jose Ferreira wrote:Great question!

Statement 1:
x can equal 0 or 2 and satisfy this equation, so it must be insufficient.
(0)^2=2(0)
(2)^2=2(2)

Statement 2:
x can equal 0 or sqrt3 or -sqrt3
(0)^3=3(0)
(sqrt3)^3=(sqrt3)^3

Put the statements together, and we see that the only number that satisfies both equations is 0. So, the answer to the original question is "No", but you cannot confuse an answer of "No" is a lack of sufficiency.

The Answer is C[/list]
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by awesomeusername » Sun May 17, 2009 9:30 am
Hello Jose,

Thank you for your explanation! I too gave the same explanations, but GMAC had the wrong explanation for (2), so I just wanted to make sure it wasn't me.
Constant dripping hollows out a stone.
-Lucretius
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by awesomeusername » Sun May 17, 2009 9:31 am
AJ, for (1), x can be 0 or 2. Forgetting the 0 is the tricky part.
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by dmateer25 » Sun May 17, 2009 9:32 am
awesomeusername wrote:Hello Jose,

Thank you for your explanation! I too gave the same explanations, but GMAC had the wrong explanation for (2), so I just wanted to make sure it wasn't me.
I was just going to mention that! I took a gmatfocus test last night and had this question.

GMAC OE says that for statement 2, x is 0, 3, or -3 which is clearly wrong.
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by Jose Ferreira » Sun May 17, 2009 9:37 am
Yes, that's exactly right AJ. You always have to check for restrictions on the variable in data sufficiency. In this question, they simply ask you whether x>0. We can safely assume that x can be positive, negative, or zero. Many times, that is not the case (i.e. "X is a positive integer..."), but when there are no restrictions, you can't forget about the possibility of the variable being 0.
Last edited by Jose Ferreira on Wed May 20, 2009 10:16 am, edited 1 time in total.
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by cubicle_bound_misfit » Sun May 17, 2009 2:51 pm
Hi Jose,

I can not get this stmt,

x can equal 0 or sqrt3 or -sqrt3
(0)^3=3(0)
(sqrt3)^3=(sqrt3)^3

stmt 2 says

x^3 = 3x

then why we are going for a avlue like 1.732 ? is not x an integer?
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by Jose Ferreira » Wed May 20, 2009 10:34 am
That's correct. The question does not specify that x is an integer. So, both sqrt3 and -sqrt3 are valid values for x given statement 2.
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