gmat club DS

[bblast]

What is the value of integer J ?

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

D

[smackmartine]

IMO D

Asked : Whats the value of J?

1) |J| = J^-1 = 1/J

if J>0 , J=1/J => j^2 = 1 => J=1
if J<0 , J= - 1/J => j^2 = -1 (Square of any number can never be negative so we cannot consider this case)

So , J=1 Sufficient.

2) J^J =1

Because any number raise to power 0 is 1 , j=0 ,in fact 0^0 is 1
So, Sufficient.

So D

[VivianKerr]

The key here is to recognize that |J| will always be positive.

J^-1 = 1/J

So J = 1/J. It has to be +1. SUFF.

[sourabh33]

I have a small doubt here.

In Equation 2

J^J = 1

J could be either 1 or 0 because both 0^0 and 1^1 will be equal to 1, and therefore statement 2 should be insufficient

Shouldn't the answer be A for this?

[sourabh33]

The answer could be D only if we consider 0^0 as undefined.

https://www.math.utah.edu/~pa/math/0to0.html
https://www.math.hmc.edu/funfacts/ffiles/10005.3-5.shtml


but google says 0^0 is 1
https://www.google.co.in/search?aq=1&oq= ... he+power+0

[VivianKerr]

Good question!

Any nonzero number raised to the power 0 is 1. 0^0 = indeterminate.