1. Jill is more beautiful than Jane == CORRECT
2. Jill is more beautiful than Jane is === CORRECT
Now , the question comes which one to use ?... actually both the answer choices are correct because " is " is implied in the first sentence. If the tense before "than" and after than" were different , than we may need supporting verb after Jane.
3. Jill is more beautiful than is Jane. (This variation was a correct answer on Princeton practise questions.. and they called #1 incorrect.)
The above sentence is correct gramatically, and even "jane is " after than is also correct, but the GMAT would prefer construction which is consice which is
Jill is more beautiful than jane ,so if the answer choices are given always chooise the one without verb, because the verb is implied in these two sentences
The crux is that .. the meaning of the sentence and what is compared should be clear and it is clear with any of the three options ( 1,2 or 3 stated above )
4. Jill is more beautiful than Jim is handsome == correct
5. Jill is more beautiful than sharp == wrong , we are not comparing sharp and jill...we want to compare the sharpness of jill with her beauty, I think the correct construction should be like " Jill is more beautiful than she is sharp "
6. Jill is more beautiful than is sharp.== wrong , same as above
7. Jill is more beautiful than she is sharp. === correct
Three important points for comparision
Meaning must be clear.
The entities being compared must be grammatically and logically parallel.
Helping verbs may not be repeated if both verbs are supposed to be in same tense
I have tried to explain this with my best possible knowledge, and am open to suggestions and improvement... ultimatly i am also here to learn