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

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

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Updated on: 29 Jun 2014, 04:32
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55% (hard)

Question Stats:

57% (00:48) correct 43% (00:56) wrong based on 201 sessions

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

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

(2) J^J = 1

I was working in this problem

What is the value of integer J?

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

The answer is D, but I thought B could have two values, 0 and 1.

Originally posted by ashish8 on 23 Jul 2012, 15:39.
Last edited by Bunuel on 29 Jun 2014, 04:32, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: If J#0, what is the value of J ?  [#permalink]

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09 Aug 2012, 04:34
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ashish8 wrote:
I was working in this problem what-is-the-value-of-integer-j-1-j-j-1-2-j-j-81006.html. The answer is D, but I thought B could have two values, 0 and 1.

QUESTION YOU ARE TALKING ABOUT 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.

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

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23 Jul 2012, 17:16
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0^0 is equal to 1 in most mathematical conventions, but not all. Therefore, you can expect that GMAT not to test the subject--it won't show up, and you won't be expected to know it!
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Re: If J#0, what is the value of J ?  [#permalink]

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02 Aug 2012, 03:06
GMAT never touches a topic which is not widely accepted. So, I dont think so that value of 0^0 will be the deciding factor in any GMAT Quant question.

Meanwhile, I made a search for the same in internet. Interesting read:

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

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09 Aug 2012, 08:28
Thank you Bunuel....
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Re: If J#0, what is the value of J ?  [#permalink]

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16 Jun 2016, 00:40
I have a doubt in this solution (could be dumb ) but im still asking. I landed up with Option B , but how is Statement 1 alone sufficient ?
I mean can't fractions also be considered in statement 1 and couldnt Abs value of 1/2 = 2^-1 ? (i mean isnt that mathematical right)
All i could say was that J is definitely positive .. I got 1 as well but I had this fraction option too so didn't go for Statement 1.
Is it wrong to consider the fraction ? i dont know if im trying to be too analytical over this but don't want to make this mistake going into the exam
Could some one pls pls help.
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Re: If J#0, what is the value of J ?  [#permalink]

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16 Jun 2016, 07:04
1
jodoubt wrote:
I have a doubt in this solution (could be dumb ) but im still asking. I landed up with Option B , but how is Statement 1 alone sufficient ?
I mean can't fractions also be considered in statement 1 and couldnt Abs value of 1/2 = 2^-1 ? (i mean isnt that mathematical right)
All i could say was that J is definitely positive .. I got 1 as well but I had this fraction option too so didn't go for Statement 1.
Is it wrong to consider the fraction ? i dont know if im trying to be too analytical over this but don't want to make this mistake going into the exam
Could some one pls pls help.

No, the math is not correct. If J = 1/2, then: $$|J| = \frac{1}{2}$$ but $$J^{-1}=(\frac{1}{2})^{-1}=2$$.
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Re: If J#0, what is the value of J ?  [#permalink]

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22 Jun 2016, 02:17
Bunuel wrote:
jodoubt wrote:
I have a doubt in this solution (could be dumb ) but im still asking. I landed up with Option B , but how is Statement 1 alone sufficient ?
I mean can't fractions also be considered in statement 1 and couldnt Abs value of 1/2 = 2^-1 ? (i mean isnt that mathematical right)
All i could say was that J is definitely positive .. I got 1 as well but I had this fraction option too so didn't go for Statement 1.
Is it wrong to consider the fraction ? i dont know if im trying to be too analytical over this but don't want to make this mistake going into the exam
Could some one pls pls help.

No, the math is not correct. If J = 1/2, then: $$|J| = \frac{1}{2}$$ but $$J^{-1}=(\frac{1}{2})^{-1}=2$$.

Oh man right the math is wrong, J stands for the whole fraction itself !!!! thanks a lot Bunuel, your awesome ...
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Re: If J#0, what is the value of J ?  [#permalink]

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17 Oct 2017, 19:27
Bunuel For this question I substituted J^2 instead of |J| so the first statement would become J^3=1. This is correct?
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Re: If J#0, what is the value of J ?  [#permalink]

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17 Oct 2017, 21:19
Amerendra wrote:
Bunuel For this question I substituted J^2 instead of |J| so the first statement would become J^3=1. This is correct?

How can this be correct? Does |x| = x^2, for any value of x?
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Re: If J#0, what is the value of J ? &nbs [#permalink] 17 Oct 2017, 21:19
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# If J#0, what is the value of J ?

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