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

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

(2) J^J = 1

[Reveal] Spoiler:
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.
[Reveal] Spoiler: OA

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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New post 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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New post 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:

http://www.askamathematician.com/2010/1 ... -disagree/
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Re: If J#0, what is the value of J ? [#permalink]

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New post 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.

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

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New post 09 Aug 2012, 08:28
Thank you Bunuel.... :-D :-D

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

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New post 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 :cry:
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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New post 16 Jun 2016, 07:04
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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 :cry:
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 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 :cry:
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 ... :-D

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

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New post 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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New post 17 Oct 2017, 21:19

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Re: If J#0, what is the value of J ?   [#permalink] 17 Oct 2017, 21:19
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If J#0, what is the value of J ?

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