Concept-The question tests on Overlapping Sets

Solution:

The problem in this question is that one writes a very general Venn diagram with an intersection region here.

Since Biology is a science already, it will be fully inside the Science circle.

Biology is a Science is a fact and not an assumption.

St(1)-28 percent of the students at University X are enrolled in a biology course.

This means that the 28% would also include Science and Biology and not only Biology as Biology is also a Science(fact not assumption).

However, we do not know the percentage of students enrolled in a science course.

If all the students ,that is 100% are in a Science course then 100-28=72% would be enrolled in Science without Biology and

If 50% of the students are in the Science course, then 50-28=22% would be enrolled in Science without Biology.

Hence no definite answer is possible unless we know the percentage of students in Science.(Insufficient)



St(2)-70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course.

On similar lines like St(1),

Lets say all the students that is 100% are enrolled for a Science Course

=> 100- 70 = 30% are enrolled in a Science without Biology and

If 50% of the students are in the Science Course, then
50-70%of 50

=50-35

=15% are enrolled in a Science without Biology.

Hence no definite answer is possible

(Insufficient)


Combining them,

Let x be the percentage of students enrolled for a Science Course

=>28 percent of the students at University X are enrolled in a biology course

(This will be a percentage belonging to Science enrollments)

and

70 percent of the students at University X who are enrolled in a science course are enrolled in a biology course

=>0.7x are enrolled in Biology

=>0.7x =0.28

=> x =0.4 =40%

=>Percentage of students enrolled in Science =40%

=>Percentage of students enrolled in Science but not in Biology

= 40 - 28

= 12%
(Sufficient)

 (option c)