Our target question is; How many of the students in a certain class are taking both a history and a science course?

Let the number of students taking history = h
Let the number of students taking science = s
Let the number of students = t
Let the number of students taking both course = b
Let the number of students not taking any of the course = n
t = h + s - b + n

Statement 1: Of all the students in the class, 50 are taking a history course.
The value of s is unknown, hence, statement 1 is NOT SUFFICIENT.

Statement 2: Of all the students in the class, 70 are taking a science course.
The value of "h" is unknown, hence, statement 2 is NOT SUFFICIENT.

Combining both statements together:
h=50, and s=70
t = h + s - b + n
t = 50 + 70 - b + n
The total number of student (t) and number of students not taking any of the course (n) are unknown. Hence, the target question cannot be answered.
Therefore, both statements combined together are NOT SUFFICIENT.

Answer = option E