Anyone is singular, so we will use his / her. I think his is more common than her.

That's what I thought too. But according to dictionary.com, that's not always the case.

their:

2. (used after an indefinite singular antecedent in place of the definite masculine form his or the definite feminine form her): Someone left their book on the table. Did everyone bring their lunch?


Does this mean either one is correct?

In GMAT this is wrong. Someone, anyone, everyone is singular, thus the pronoun should also be singular.

Did everyone bring his lunch?
Someone left her book on the table.

Nailya wrote:In GMAT this is wrong. Someone, anyone, everyone is singular, thus the pronoun should also be singular.

Did everyone bring his lunch?
Someone left her book on the table.

So is the GMAT right in making this wrong? I guess there could be an argument since both could be technically right.

I think it's ok in conversational speech, as for the GMAT we better play the game by its rules:-)

Over here IMO SANAM rules as mentioned in Manhattan applies....

SANAM = Some, Any, none, All, Most...

All the above can be singular or plural in GMAT depending on the context. It depends on the object after of....Both the below IMO are correct:

a) Some of the apples "were" wrong.
b) Some portion of the apple "was" rotten.

Thanks
Mohit

Some of, most of, etc are indeed depend on whether the word following the "of" is single or plural, but everyone, someone is always single. Manhattan SC explains it.

yes....thanks for correcting me.

No prob