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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:

https://www.askamathematician.com/2010/1 ... -disagree/
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Thank you Bunuel.... :-D :-D
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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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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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Bunuel
jodoubt
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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I was working in this problem https://gmatclub.com/forum/what-is-the-v ... 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.

Hi Bunuel,

Please help me understand, why |j| won't have two values? Nowhere in question it is mentioned that J can't be negative
|J| = j^-1
2 conditions:
j = j^-1 and j = - j ^-1
Why its incorrect? I am sorry I do not understand this
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Bunuel
ashish8
I was working in this problem https://gmatclub.com/forum/what-is-the-v ... 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.

Hi Bunuel,

Please help me understand, why |j| won't have two values? Nowhere in question it is mentioned that J can't be negative
|J| = j^-1
2 conditions:
j = j^-1 and j = - j ^-1
Why its incorrect? I am sorry I do not understand this

j cannot be negative. If j = negative, then |j| = positive and j^(-1) = negative. So, |j| ≠ j^(-1). Therefore, the only case we could have is when j is positive and thus |j| = j, and the equation transforms only to j = j^(-1).
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ashish8
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.

Hi Bunuel VeritasKarishma

I am getting j = 1 or j = -1 using below approach for statement 1.

|j| = j^-1 = 1/j

therefore 2 cases are possible as below:

j = 1/j or j = -1/j

j^2 = 1 or j^2 = -1

Since square of any number cannot be negative j^2 = -1 is discarded.

Hence answer is j^2 = 1 --> j = 1 or j = -1

Please correct where my conceptual gap.
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Patilsv28
ashish8
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.

Hi Bunuel VeritasKarishma

I am getting j = 1 or j = -1 using below approach for statement 1.

|j| = j^-1 = 1/j

therefore 2 cases are possible as below:

j = 1/j or j = -1/j

j^2 = 1 or j^2 = -1

Since square of any number cannot be negative j^2 = -1 is discarded.

Hence answer is j^2 = 1 --> j = 1 or j = -1

Please correct where my conceptual gap.

First read this post:

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/0 ... -the-gmat/

When you take positive and negative values, you must keep the ranges in mind.

j = 1/j (when j >= 0)
or j = -1/j (when j < 0)

When the first equation gives you two values 1 and -1, you know for a fact that j cannot be -1 because this equation holds only when j >= 0.
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