Arthur and Martha have preferences over two goods - beer and pizza. Matha pays twice as much for both beer and pizza when compared to Arthur's price. Arthur and Martha both claim that they have achieved highest possible utility, subject to their individual budget constraints. Which of the following statements are necessarily true?

A. They both have the same marginal utility of beer

B. They both have the same marginal utility of pizza

C. Arthur's marginal rate of substitution of beer for pizza is smaller than Martha's marginal rate fo substitution of beer for pizza

D. They both have the same marginal rate of substitution of beer for pizza

E. Arthur's marginal rate of substitution of beer for pizza is larger than Martha's marginal rate of substitution of beer for pizza