GMATMadeEasy wrote:Megumi speaks Japanese better than I do.
Megumi has visited more countries than I have.
Megumi has more skirts than I do.

I have never seen an aardvark, but last year my father DID.
I have never seen an aardvark, but last year my father saw one.

Could someone explain how to decide second part verb and/or auxiliary verb ?

You are not required to repeat the auxiliary verb if the following matters are true:

1. if there is no tense shift.
2. If there is no ambiguity.

Example:
Megumi has visited more countries than I.

--> This sentence does not require to use the auxiliary verb in the second half because:
1. meaning is clear.
2. there is no tense shift.

I have never seen an aardvark, but last year my father did.

--> This sentence needs the second auxiliary verb because:
1. There is a tense shift.

Thanks.

is it correct ?

I have never seen an aardvark, but last year my father did.

GMATMadeEasy wrote:is it correct ?

I have never seen an aardvark, but last year my father did.

Yes, it's correct. The "ambiguity" one is the harder one to catch, too, since it's hard to make rules for it. If the verb in the comparison is transitive -- if it has a direct object, like "Bob called Joe before Barb" -- be especially watchful for possible ambiguity. Intransitive verbs -- like verbs of being -- are less ambiguous: "Bob is taller than Joe". Note that it's not grammatically incorrect to repeat the verb, but the GMAT can nail you on concision if the question is a tricky one.

Thanks but From the source I have taken it , it is incorrect.

I have never seen an aardvark, but last year my father did.

Because tense shift needs the proer verb in later part. is this reasoning wrong ?