Question

In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is

• A. 18
• B. 20
• C. 24
• D. 32

Hint:

Use inclusion-exclusion for the two subjects, then add the students who like neither: (10 + 12 - 4) + 6.

Answer 1

The Correct Option is C

Step 1: Break the group into four separate, non-overlapping regions.
Instead of using the inclusion-exclusion formula directly, split the students into four categories that do not overlap with each other: students who like only Mathematics, students who like only English, students who like both subjects, and students who like neither subject. Adding these four disjoint counts gives the total group size.

Step 2: Find the "only Mathematics" count.
10 students like Mathematics in total, and 4 of those also like English. So the students who like Mathematics and nothing else are
$10 - 4 = 6$

Step 3: Find the "only English" count.
12 students like English in total, and the same 4 students who like both are already counted inside that 12. So the students who like English and nothing else are
$12 - 4 = 8$

Step 4: Add up all four regions.
Only Mathematics = 6, only English = 8, both subjects = 4, neither subject = 6. None of these four groups overlaps with any other, so the total group size is simply their sum:
$6 + 8 + 4 + 6 = 24$

Final Answer:
The group has 24 students, matching option (C).