A combined average of two sets is the sum of all measurements over the total number of measurements.

The sum of $300$ measurements of the data set with arithmetic mean $72$ is $300 \cdot 72 = 21600$.
The sum of $200$ measurements of the data set with arithmetic mean $64$ is $200 \cdot 64 = 12800$.
Thus the sum of all measurements is $21600 + 12800 = 34400$ and the total number of measurements is $500$.
The arithmetic mean of the $500$ measurements is $\frac{34400 }{ 500} = 68.8$, which is greater than $68$.
Hence, A is greater than B.

Therefore, A is the right answer.