Does Bond Valuation use Yield to Maturity or Expected Rate or Return?

I am learning basic finance, and while working through some practice problems, I ran into some problems.
The question is:
A year ago, I bought two bonds by the same company. One is a 20 year maturity with $1000 par value, with annual coupon of 7%, and the second one is a 5 year maturity with the same par value and same coupon rate. Both had a yield to maturity (=required rate of return) of 9% when I bought them.
b. Today, assume the yield to maturity on both bonds is 11%. What is the total rate of return on each bond if you sell these bonds today?
c. now imagine today’s yield to maturity is 13% for each bond. What is the total rate of return on each bond if you sell these bonds today?

So basically, assuming that we use the required rate of return to compute bond prices, we would have the same answer for both questions. The professor gave us different YTM values, which seems to suggest that we need to use YTM, but using YTM values actually drops the bond price further away from the par value, which doesnt make sense. But if we use the same 9% required rate, the answer is substantially the same.

What am I missing here?