aramjung wrote:

Is \(\frac{7^7}{7^x}\) an integer?

(1) \(0\leq{x}\leq{7}\)

(2) \(|x|=x^2\)

stmt1: x can be fraction between 0 to 7 so insuff.

stmt2: |x| = x^2

-x = x^2 => x(x+1) = 0 => x = 0 or x = -1

or

x = x^2 => x(x-1) = 0 => x = 0 or x = 1

in any of the three cases 0, 1 , -1 it is going ot be an integer to sufficient.

Hence, B is the answer.

it cannot be fraction all the way, take for example x = 1/2 it is between 0 to 7 but 7^7/7^1/2 is not an integer

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My debrief: done-and-dusted-730-q49-v40