Statistics Major and Math Minor Sufficient for Data Science

In order to enter a Data Science graduate program, are a these two efficient along with a few Math Modeling classes, an Intro Programming Class and a Visualization and Data Analysis class?

Maybe. It depends on the program - some data science programs might have more heavy computer science/programming coursework requirements. Check out the prerequisites on the website; most data science programs give some indication as to how much math/statistics and how much programming/computer science coursework they expect you to have. For some programs this would be fine and for others it might not be enough.