Which genus is found in the fayum and is probably close to the ancestry of both major groups of living old world anthropoids?

The correct answer is the Aegyptopithecus

The Aegyptopithecus, also known as the Egyptian Monkey, was one of the early catarrhines who predated the difference between hominoids, which are the apes and the humans, and cercopithecids, which are known as the old world monkeys. It is called the Egyptian monkey because its fossils were found mostly in Egypt.