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

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Manager
Joined: 28 Feb 2003
Posts: 100
What is the value of x? 1) x^x = 2x 2) = x^2 is modulus [#permalink]

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23 May 2003, 19:45
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What is the value of x?

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

[..] is modulus
Manager
Joined: 28 Feb 2003
Posts: 100

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28 May 2003, 02:32
sorry skoper,
I think you are right......the answer should be A

I am sorry again.....don't know how i screwed up
Intern
Joined: 30 Apr 2003
Posts: 2
Location: Zanzibar

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28 May 2003, 13:35
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
_________________

Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's law.

Manager
Joined: 25 May 2003
Posts: 54

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28 May 2003, 14:14
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?
Intern
Joined: 25 May 2003
Posts: 17
Location: Thailand

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01 Jun 2003, 22:55
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
Joined: 19 Jun 2003
Posts: 151
Re: GMAT-DS: one more chance to catch x [#permalink]

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15 Jul 2004, 14:20
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
Joined: 21 Mar 2004
Posts: 445
Location: Cary,NC

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15 Jul 2004, 14:28
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
_________________

ash
________________________
I'm crossing the bridge.........

Manager
Joined: 16 May 2004
Posts: 64
Location: columbus

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15 Jul 2004, 16:24
[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
Intern
Joined: 07 Jun 2004
Posts: 29
Location: Sunnyvale

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15 Jul 2004, 16:27
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.
_________________

Davefor MBA

Manager
Joined: 21 Jun 2004
Posts: 52

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15 Jul 2004, 20:55
Thats for the detailed explination Dave
Manager
Joined: 19 Jun 2003
Posts: 151

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15 Jul 2004, 22:25
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
Joined: 05 Jul 2004
Posts: 894

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16 Jul 2004, 12:31
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)..
Senior Manager
Joined: 21 Mar 2004
Posts: 445
Location: Cary,NC

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16 Jul 2004, 12:40
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 )
_________________

ash
________________________
I'm crossing the bridge.........

Senior Manager
Joined: 07 Oct 2003
Posts: 350
Location: Manhattan

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16 Jul 2004, 14:02
could someone confirm that 0^0 is an unreal number as far as GMAT is concerned?

16 Jul 2004, 14:02
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