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# If J#0, what is the value of J ?

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Director
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If J#0, what is the value of J ? [#permalink]

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26 Aug 2005, 00:55
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If $$J\neq{0}$$, what is the value of J ?

(1) |J| = J^(-1)

(2) J^J = 1

what is the value of integer J

1: | J | = J ^ -1
2: J^J = 1

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-j-0-what-is-the-value-of-j-136223.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Jun 2014, 04:35, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If J#0, what is the value of J ? [#permalink]

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26 Aug 2005, 06:45
from i, | J | = J^(-1)
j=1/j
j^2=1, so j must be 1.

fro ii, J^J = 1. the only integer whose power is itself is equal to 1 is 1. so D.
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Re: If J#0, what is the value of J ? [#permalink]

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26 Aug 2005, 08:37
HIMALAYA wrote:
from i, | J | = J^(-1)
j=1/j
j^2=1, so j must be 1.

fro ii, J^J = 1. the only integer whose power is itself is equal to 1 is 1. so D.

Himalaya,
Souldn't it be B, because Condition 1) gives +/- 1
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Re: If J#0, what is the value of J ? [#permalink]

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26 Aug 2005, 08:45
No 0^0 = 1 as well

So (ii) has two solutions, 0 and 1.

whereas (i) only has one solution 1.

So A
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Re: If J#0, what is the value of J ? [#permalink]

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26 Aug 2005, 08:48
isn't 0^0 undefined? so cannot be solution?
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Re: If J#0, what is the value of J ? [#permalink]

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26 Aug 2005, 13:42
0^0=0...

x^0=1

for GMAT math that is....
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Re: If J#0, what is the value of J ? [#permalink]

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26 Aug 2005, 14:25
i just did 0^0 on calculator and it has error message...also kaplan book says its undefined. is this typo?
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Re: If J#0, what is the value of J ? [#permalink]

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26 Aug 2005, 16:10
0^0 is undefined...cannot ask that in GMAT so B is for sure...

But guys How about A? doesn't that give J = +/- 1.
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Re: If J#0, what is the value of J ? [#permalink]

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27 Aug 2005, 00:21
No (-1)^(-1) = -1
but mod (-1) = 1
So -1 does not satisfy the first equation.
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Re: If J#0, what is the value of J ? [#permalink]

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28 Aug 2005, 12:04
this was also my problem guys. the value of 0^0. My own calculator (windows XP sci. calc) tells me it is 1, so my choice was (A), but the OA is (D).

So, what is the GMAT value of 0^0?
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Re: If J#0, what is the value of J ? [#permalink]

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28 Aug 2005, 17:25
0^0, 0/0 etc are mathematically undefined, it is not just a GMAT fact. There may be slightly different rules for verbal in GMAT but laws of maths can't be changed.
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Re: If J#0, what is the value of J ? [#permalink]

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29 Aug 2005, 09:20
Axioms of mathematics can indeed be changed.

It is perfectly reasonable to treat 0^0 = 1.
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Re: If J#0, what is the value of J ? [#permalink]

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29 Jun 2014, 01:01
My calculator says 0 ^ 0 is 1

If we consider stmt 1 | j | = 1 / j then j has to be only j = 1 .
stmt 2 j^j = 1 then j =0 or 1 .
Then OA is a could some one comment on this ???

I am totally confused !!
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Re: If J#0, what is the value of J ? [#permalink]

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29 Jun 2014, 04:34
shelrod007 wrote:
My calculator says 0 ^ 0 is 1

If we consider stmt 1 | j | = 1 / j then j has to be only j = 1 .
stmt 2 j^j = 1 then j =0 or 1 .
Then OA is a could some one comment on this ???

I am totally confused !!

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.

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-j-0-what-is-the-value-of-j-136223.html
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Re: If J#0, what is the value of J ?   [#permalink] 29 Jun 2014, 04:34
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