I'm studying at the Hopkins-Nanjing Center this year and will enroll in the MA program at SAIS next year. My only SAIS experience so far has been taking microeconomics in DC during pre-term in August. I did met a lot of 1st year students over the summer and there were a number of students who were straight out of undergrad. The majority had 2-5 years of work experience.
The website currently says "middle 50% GRE verbal score range has been 158-165 (79th - 96th percentile) and the middle 50% GRE quantitative score range has been 154 - 161 (67th - 86th percentile). For the GMAT verbal score, the middle 50% has been in the 34-42 range, and the GMAT quantitative score has been in 38-49 range.
If you're curious to see what the average scores for SAIS were for the old GRE exam, it was 729 Q, 650 V and for the GMAT it was 41V, 46Q (I saved this info on my computer when researching schools a couple years ago).