How many pass only one subject?

• A. 3
• B. 12
• C. 9
• D. 15

Answer: (C)

Count how many people are in exactly one subject by focusing on the single-subject regions in a three-subject Venn diagram. For any subject, the number who pass that subject and not the others is found by taking all who pass that subject, removing those who also pass another subject, and then adding back those who pass all three (to correct for over-subtraction). Do this for each subject and add the three results.

In symbols, with subjects A, B, and C: the total who pass only one subject equals (|A| − |A∩B| − |A∩C| + |A∩B∩C|) + (|B| − |A∩B| − |B∩C| + |A∩B∩C|) + (|C| − |A∩C| − |B∩C| + |A∩B∩C|). When you plug in the problem’s counts for each subject, their pairwise overlaps, and the all-three overlap, you get 9.

So the correct result reflects the sum of the three single-subject regions after accounting for overlaps.