DKP is right It sure is an elliptical statement. When you have sucha doubt try extending the sentence with the same verb that was used earlier in the sentence with reference to the subject. Your sentence does not sound right becasue when you extend it 'she sings better than me' cannot be extended to ...better than me can? Consider this He is taller than me or I . Extended it will read He is taller than me 'is' or personal pronoun 'am'. Both are incorrect. Try the sentence with I am.
Hi Erin - unfortunately "preferences" dont enter into the GMAT ..its either correct or incorrect... this sentence has to do with the use of objective or subjective pronouns and their use
example : he is taller than me WRONG
he is taller than I CORRECT
if in doubt invert the object and subject to see if it makes sense......
I am taller than he is
NOT ...me am taller than he is