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# M04 DS # 11

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Re: M04 Q11 [#permalink]  21 Aug 2009, 18:53
I'd like to toss in my vote for option A.

S1 suffices to indicate that J=1 only.

In S2, J^J=1 is ambiguous: 1^1 certainly works. The math sources I consulted a while back acknowledged that 0^0=1 is a little counter-intuitive, but makes sense because x^0 is a much more frequently encountered function than 0^y. Therefore, keeping x^0 continuous with neighboring values (x^0=1 for sure if x<>0) is higher priority than keeping 0^y continuous with neighboring values (0^y=0 for sure if y>0). Naturally I defer to actual mathematicians. However, when (apparently real) mathematicians say that defining 0^0=1 is more in keeping with the pragmatism that underlies many other mathematical conventions in what is in many ways a language constructed by humans, I find their arguments very compelling.

A previous poster, GMAT Tiger, mentioned that the GMAT regards 0^0 as undefined. If anyone has an OG reference for that, I'd be glad to read it. At present, I rather hope that the GMAT will not specifically test something so contentious.
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Re: M04 DS # 11 [#permalink]  19 Jul 2010, 04:06
GMAT TIGER wrote:
topmbaseeker wrote:
What is the value of integer J ?

1. |J| = J^{-1}
2. J^J = 1

(C) 2008 GMAT Club - m04#11

1. |J| = J^{-1}
|J| = 1/J
so only possible value for J = 1.

2. J^J = 1
J^J = 1 . Here also only possible val;ue for J = 1.

So it is D.

I agree with GT, Answer is D.
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Re: M04 DS # 11 [#permalink]  19 Jul 2010, 04:12
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Re: M04 DS # 11 [#permalink]  19 Jul 2010, 04:28
The answer is D for both (1) and (2) are equivalent of J=1.

0^0 is and must be undefined for several reasons.
First, if you consider the Y=X^X function at any real rather than integer X you will notice, that however close X is to 0 the value of X^X is never close to 1.
Second, X^X is equal to e^(X*lnX), which is clearly undefined at X=0 as lnX is undefined at zero.

And of course, calculators are not of much help when it's about definitions, like google translator just translates whatever you type and never tells that you enter a gramatically wrong sentence.

Good luck!

Last edited by AntonValkov on 19 Jul 2010, 11:58, edited 1 time in total.
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Re: M04 DS # 11 [#permalink]  19 Jul 2010, 07:02
"Consensus has recently been built around setting the value of 0^0 = 1"
http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
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Re: M04 DS # 11 [#permalink]  09 Aug 2010, 05:00
D too.

(Base of 0 always yields 0 regardless of its exponent - MGMAT)
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Re: M04 DS # 11 [#permalink]  21 Jul 2011, 05:02
good question! but since 0^0 is debatable I doubt if this concept will appear in GMAT.
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Re: M04 DS # 11 [#permalink]  21 Jul 2011, 16:06
D for me since 0 raised to the power 0 is invalid. Only +1, -1 values are narrowed down for each, of which only +1 works.

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Re: M04 DS # 11 [#permalink]  21 Jul 2011, 21:45
both statements solve the problem uniquely and resulted in +1.
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Re: M04 DS # 11 [#permalink]  27 Sep 2011, 02:49
controversial
answer could be A since many mathematicians take 0^0 =1
but D is also possible if the above is not the case.

I wonder what the official GMAT view is?
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Re: M04 DS # 11 [#permalink]  09 Mar 2012, 04:28
|J| = J^{-1}

This gives us two equations

eqn 1
J=1/J

i.e, J^2 = 1
Therefore, J= +1 or - 1

eqn 2
-J= 1/J
i.e, J^2= -1
Therefore J= SQRT(-1)

How to proceed?
Is SQRT(-1)=1? Even if this value is 1 we will still have another value -1 that we got from eqn 1 right?
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Re: M04 DS # 11 [#permalink]  09 Mar 2012, 06:54
Expert's post
topmbaseeker wrote:
What is the value of integer J ?

1. |J| = J^{-1}
2. J^J = 1

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

This question needs revision, it should state that J does not equal zero.
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Re: M04 DS # 11 [#permalink]  25 Jul 2012, 14:27
I would like to highlight a common "gotcha" when dealing with solutions involving absolute values.
|J| = 1/J (By the way (J ^ -1) = 1/J)
This equation may seem to have 2 solutions
J = 1/J (OR) -J = 1/J
J^2 = 1 (OR) J^2 = -1

Of the above, only J^2 = 1 makes sense.
This equation has 2 solutions, i.e J = +1 or -1, HOWEVER the uniqueness of absolute value equations is that
some of the solutions may NOT satisfy the original equation. One has to substitute the options BACK
into the original equation to check the feasibility.
In this case, J = -1 doesn't satisfy the original equation (which is |J| = 1/J) , hence J = +1 is the only solution.

Be wary of equations involving absolute values ! Always substitute the answer choices back into the equation to evaluate
the feasibility
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Re: M04 DS # 11 [#permalink]  25 Jul 2012, 17:20
Good one. I have read the explanations above and found them to be plausible. I rejected 0^0 as invalid and hence got 1 as the value of J for both the statements. hence chose D.

A few guys have said that GMAC will not test 0^0 and I am of the same opinion.
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Re: M04 DS # 11 [#permalink]  25 Jul 2013, 05:52
Expert's post
BELOW IS REVISED VERSION OF THIS QUESTION:

If j\neq{0}, what is the value of j ?

(1) |j| = j^{-1}
(2) j^j = 1

(1) |j| = j^{-1} --> |j|*j=1 --> j=1 (here j can no way be a negative number, since in this case we would have |j|*j=positive*negative=negative\neq{1}). Sufficient.

(2) j^j = 1 --> again only one solution: j=1. Sufficient.

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Re: M04 DS # 11   [#permalink] 25 Jul 2013, 05:52
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