An astronomer notices two stars in the Milky Way Galaxy. He calculates that Star X is closer to Earth than Star Y. He then records that both stars have the same brightness. What definitely can be concluded about the two stars?

Luminosity of the two stars is the same.

Explanation:

It is given that Star X is closer to Earth than Star Y therefore even if the luminosity of these two stars is same, the one that is near to earth will appear brighter as compared to the other distant star.

The brightness of a star is directly proportional to the square of the distance between the stars and observant.  

Here in the case the as the distance gets  doubled the brightness becomes four times  

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