If and $ (10+\log _{10}x), (10+\log _{10}y)$ are $(10 + log_{10}z)$ in AP, then consider  the following statements:

I. The GM of x and z is $y ^ 2$

II. The AM of $ \log _{10}x$ and $ \log _{10}z$ is $log_{10} y $

Which of the statements given above is/are correct?