math problem?

Question

The arithmetic mean (average) of two numbers, one of which is q, is pq. If a third number is added, the arithmetic mean of all three numbers is p+2pq/3 Which of the following represents the third number?

2p-q
q-p
3(q+p)
pq
p

Answer 1

2p-q

Answer 2

If the mean is p + 2 pq/3, then the sum is 3p + 2pq

But the sum of the first two alone is twice their mean = 2pq

So the third one is 3p.

Unfortunately, that's not one of the answers proposed, so either I made an error or you made a typo.

Interestingly, I didn't use the fact that one of the numbers is q, because I didn't have to.

So I suspect you of a typo.