He used the Henderson-Hasselbach equation.
Here's a picture with a full rundown:
http://i.imgur.com/sS3av3C.png
The key thing to recognize here is that you're starting with a buffer of a pH between 4.5 and 5 (you wouldn't be expected on the MCAT to be able to calculate this exactly) and that you're not adding that much acid - so you're still in the buffer region. Meaning the pH is still close to where you started.