But are the writers smarter than a 5th grader?

So I'm gliding along on my new Tony Little Gazelle, and watching bad tv. And the question on Are You Smarter Than a 5th Grader? was "how many adjectives are in the sentence 'Spencer takes good care of his hairy dog.'"

The answer given was 2, which they said was correct, but I'm 99% sure it's 3.

Spencer is a proper noun
takes is a verb
good is an adjective
care is a noun
of is a preposition
his is a possessive adjective
hairy is an adjective
dog is a noun.

I think they didn't count "his." Losers.

Oh, and he won $500,000. That's not fair.