Cool question!

There's a lot of information given here, so let's eat slow here.

Joey scores a 40 at the end of his first year. That means that he's currently 20 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).

Now, come next year, or his second year at this psychology school, he's technically 21 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.

Well, his second year is then going to be 21(2) + 20 = 62.

Now let's tackle the main question: what's his grade going to be the third year?

Well, he will be at an age of 22 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (22x2), plus half of his previous year's grade (as calculated for his second year, his grade is 62; therefore, 62/2)

Having said that, the final answer would be 22(2) + 62/2 = 44 + 31 = 75 --> (D)

_________________

GMAT Club Premium Membership - big benefits and savings