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 $|M \cup E| = |M|+|E|-|M \cap E|$ to find how many like at least one subject, then add the "neither" count for the total group size.

Answer 1

The Correct Option is C

This problem is easiest to picture as a Venn diagram with two overlapping circles, one for Mathematics and one for English, sitting inside a rectangle that represents the whole group.

1. Both subjects: the overlap region has 4 students, since 4 students like both Mathematics and English.
2. Only Mathematics: out of the 10 who like Mathematics, 4 are shared with English, so $10-4=6$ students like only Mathematics.
3. Only English: out of the 12 who like English, 4 are shared with Mathematics, so $12-4=8$ students like only English.
4. Neither subject: given directly as 6 students, sitting outside both circles.

Adding up every region of the diagram gives the full group: only Mathematics (6) plus only English (8) plus both (4) plus neither (6), which is $6+8+4+6=24$.

Let's summarize:

• Only Mathematics: 6 students.
• Only English: 8 students.
• Both: 4 students.
• Neither: 6 students.

Adding all four non-overlapping regions gives a total group size of 24 students, option (C).