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# What is the value of x? 1) x^x = 2x 2) = x^2 is modulus

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Manager
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What is the value of x? 1) x^x = 2x 2) = x^2 is modulus [#permalink]  23 May 2003, 18:45
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What is the value of x?

1) x^x = 2x
2) [x] = x^2

[..] is modulus
Manager
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sorry skoper,
I think you are right......the answer should be A

I am sorry again.....don't know how i screwed up
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How ?? [#permalink]  28 May 2003, 12:35
How is it A ??
X^X = 2^X
equals
X^X - 2x = 0
or
X( X ^ (X-1) - 2) = 0
or
X = 0 or the solution of X^(X-1) -2 = 0 => X = 2
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Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's law.

Manager
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here we go again...

if x=0 is a possible solution then you're saying x^x=0, which is generally regarded to be of indeterminate form, not 0.

what does GMAC consider?
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my view [#permalink]  01 Jun 2003, 21:55
This must be in the difficult pool question. Although seeming very easy to solve both statements, the question contains so many traps wait for all of those who are under pressure.

I vote this very very cool question.

Anyway, I choose A.
Manager
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Re: GMAT-DS: one more chance to catch x [#permalink]  15 Jul 2004, 13:20
brstorewala wrote:
What is the value of x?

1) x^x = 2x
2) [x] = x^2

[..] is modulus

Could somebody please solve this ?
Senior Manager
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A. x^2 = 2x => x=0 or x=2 : A is insufficient

B. |x|=x^2

=> x>=0 becuase x^2 is >= 0
|x| = x if x>=0
so , equation is now x=x^2
=> x=0 or x=1

B is insufficient.

C. using both we get a unique answer x=0. C is sufficient.

HTH
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ash
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Manager
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ans [#permalink]  15 Jul 2004, 15:24
[quote]
here we go again...

if x=0 is a possible solution then you're saying x^x=0, which is generally regarded to be of indeterminate form, not 0.

what does GMAC consider?

[/quote]

Skoper could you please explain what you mean by indeterminate form??

I think the answer is C
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for 1)
x^2=2x can be factored as x(x-2)

Therefore x=2 or x=0

Therefore 1) is insufficient.

for 2)
|x|=x^2

The only numbers that make this statement true are 0 and 1

Therefore 2) is insufficient.

So if we put the two together,
1) tells us x=2 or 0, but since 2) tells us x=1 or 0, then the combination of two results in only one answer which is 0.

I saw your posting ashkg, but needed to rephrase it this way to make sure I got the whole concept.

If I'm mistaken, somebody please let me know.
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Davefor MBA

Manager
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Thats for the detailed explination Dave
Manager
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Thanks guys..

But both of you write (1) as x^2 = 2x

But infact it is x^x = 2x

Is there any specific reason for your interpretation that I am not seeing?

Director
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One Exerpt from the Net...

What is the value of 0^0 (^ means exponent)? Can it be considered to be the limit of a^0 as a approaches 0 ?

0^0 is indeed indeterminate. It turns out that you could make
it have any value between 0 and 1, inclusive. You could have 0 if it's the
limit as a->0 of 0^a, you could have 1 if it's the limit as a->0 of a^0,
and for x in between 0 and 1, (and this is the neat part from Dr. Shimimoto)
look at the expression (x^n)^(1/n). This just equals x for all positive
values of n. As n->Infinity, this fraction goes to 0^0, but if it's
just x the whole time, the limit of the expression as it goes to 0^0 is x.
So we could make it anything in between 0 and 1, so it's got to be
indeterminate.

Some technical crap...

In sum, I think we can't take x=0 as one of the solution.
So, the answer should be (A)..
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afife76 wrote:
Thanks guys..

But both of you write (1) as x^2 = 2x

But infact it is x^x = 2x

Is there any specific reason for your interpretation that I am not seeing?

i screwed up.......ans should be A ( assuming 0^0 is indeterminate )
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ash
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Senior Manager
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could someone confirm that 0^0 is an unreal number as far as GMAT is concerned?

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