There are 10 people in a room, consisting of men and women. The total age of all the people in the room is 240 years. The ages of all the people are distinct integers, and the age of each man is greater than the age of any woman. What is the age of the youngest man in the room?

Statements:
Statement 1: The age of the oldest woman is 30 years.
Statement 2: The age of the youngest woman is 20 years.

Statement 1 gives us that the oldest woman is 30 years old. However, this doesn't provide enough information to find the age of the youngest man because we don't know how many men are or their ages.

Statement 2 tells us that the youngest woman is 20 years old, but this also doesn't give sufficient information about the men’s ages or their total.

Even combining both statements doesn’t give us enough to calculate the youngest man’s age because we still lack the distribution of ages among the men and women.

Thus, the correct answer is (E): Both statements together are not sufficient to answer the question.