grammar - Correct use of they or them, me or I?

"May me we are not rich as (they.them),but I bet we are lot happier.
"Your husband doesn't believe that you are older than (me/I)".

I was reading from "Word Power Made Easy-by Norman Lewis" and these question struck me. In the first sentence it says the correct word in place is "they" and in second it say the correct word is "I". Both struck me in doubt cause, It seem odd to me. Are they really correct?
If yes, what is the general rule for use of these words, how can I figure out in other sentences?

Answer

The object of a proposition should be in objective case. So "as them" and "than me."

You would use "they" and "I" if the you add a verb: "as rich as they are" or "you are older than I am" because that changes it to a subordinate clause rather than a prepositional phrase. The pronoun then becomes the subject within the subordinate clause. "As" and "than" function as the subordinating conjunction.

Some people always think of "as" and "than" as subordinating conjunctions, the verb just being omitted from the clause. That sounds awkward to my ears because without a verb there is no clause; without a clause it becomes a prepositional phrase.