Let's break this down answer choice by answer choice:
I) This by itself is not enough information because we have no information about who scored what
II) This by itself is also not enough information because we have no information about the age of the students.
Since neither I nor II alone are sufficient, we can get rid of answer choices A, B, and D. Now let's take a look at answer C:
I + II together) This question can really be seen as a Venn Diagram problem, with one circle being number of students aged 21-23, and another circle being number of students scoring 70-90. The value we really want is the intersection of the circles in the middle, as shown here:
In this Venn Diagram, we know that with the 2 cases together, there are 17 total students aged 21-23 and 17 total students who scored 70-90. To find the middle area of a Venn Diagram you have to add the number of subjects in each circle individually and then subtract the total subjects all put together from that sum. In this case, 17 + 17 - total students in this situation. However, we don't have the total number of students period, and as a result are unable to find the value we want. Therefore, both statements together are NOT sufficient.
The answer is
E.