Question

The diagram below shows the number of people who attended seminars on Physics, Chemistry, Math and Biology. What is the number of people who attended exactly any two seminars? 

• A. 21
• B. 36
• C. 38
• D. 42

Hint:

For “exactly two” in Venn diagrams, add only the regions where \emph{exactly} two sets overlap and exclude all single-set and any triple/quadruple overlaps.

Answer 1

The Correct Option is B

Read the regions labelled for pairwise--only intersections (exclude singles and any region where three or four sets overlap).
From the diagram:
- Biology & Physics only \(=7\).
- Biology & Math only \(=5\).
- Physics & Math only (but not Biology or Chemistry) \(=14\).
- Math & Chemistry only (inside triangle but outside the circle/biology) \(=10\).
Triple-overlap numbers like \(4\) (B–P–M) and the central \(2\) (all four) are not counted; singles like \(6\) (B only), \(8\) (P only), \(13\) (C only) are also excluded.
\(\Rightarrow\) Exactly-two total \(=7+5+14+10=36\).
\(\boxed{36}\)