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"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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Senior Manager
Status: Yeah well whatever.
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I completely disagree. It's A. Is this GMAT prep?
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He that is in me > he that is in the world. - source 1 John 4:4
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S1: lJl = J^-1 => lJl = 1/J
So, only J=1 satisfies this equation. Then l1l = 1/1= 1.
If we put J=-1, then l-1l = -1/1=-1 => 1= -1 which does not satisfy the equation. there is only one answer for J; J=1. S1 is sufficient.
S2: J^J = 1 ; here also only J=1 satisfies the equation. So, S2 is sufficient.
Therefore, answer is D.
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I will go with "D"
(1) |J| = J^-1 which implies that, |J|=1/J
That means: J|J| = 1
This tell us that J is always positive and the only such positive number is 1
(2) Trail & Error...The only possible J value is: 1
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Manager
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either statement is suff.
Ans D
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D too.
(Base of 0 always yields 0 regardless of its exponent - MGMAT)
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Senior Manager
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RenukaD wrote:
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 value for J = 1. [[highlight]0^0=1[/highlight]] hence this cant give the unique value
So it is D.>>>>>>>>>>A ([highlight]now cant be D[/highlight])
I agree with GT, Answer is D.
Dear RenukaD hope this helps
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good question! but since 0^0 is debatable I doubt if this concept will appear in GMAT.
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D is the answer..each statement is sufficient to get J
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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. Posted from my mobile device 
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My Answer is also D.
both statements solve the problem uniquely and resulted in +1.
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both statements are self sufficient..its D for me
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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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|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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ENAFEX wrote: |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? QUESTION SHOULD READ: If J\neq{0}, what is the value of J ?(1) |J| = J^{-1}(2) J^J = 1 Two reasons why should the stem state that J\neq{0}: For statement (1) if J=0 then we'll have 0^{-1}=\frac{1}{0}=undefined. Remember you can't raise zero to a negative power. For statement (2) if J=0 then we'll have 0^0. 0^0, in some sources equals to 1, some mathematicians say it's undefined. Anyway you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT. So on the GMAT the possibility of 0^0 is always ruled out. Also notice that saying in the stem that J is an integer is a redundant. AS FOR THE SOLUTION: If J\neq{0}, what is the value of J ?(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. Answer: D. AS FOR YOUR QUESTION: If you consider J<0 for (1) you'll have: -J=\frac{1}{J} --> J^2=-1. This equation has no real roots (square root of negative number is undefined for the GMAT) and since GMAT is only dealing with real numbers then for the GMAT it has no roots ( \sqrt{-1}=i, where i is complex number/imaginary unit). Hope it's clear.
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I would like to highlight a common "gotcha" when dealing with solutions involving absolute values. Lets consider answer option a) |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 = -1Of 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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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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