120 students wrote an exam with 4 questions. 100 solved the first question, 95 the second, 90 the third, and 80 the fourth. What is the smallest possible number of students that solved all four questions?

Correct option is B

Given:
Total students = 120
Solved Q1 = 100
Solved Q2 = 95
Solved Q3 = 90
Solved Q4 = 80
We are to find the minimum number of students who solved all four questions.

Concept:

Minimum overlap (Inclusion-Exclusion Principle)
To find the minimum number of students who solved all four questions, we use this concept:

When we are given totals of each group (students who solved each question), and we want the minimum overlap (common students across all), we maximize the number of students who solved fewer than 4.

The formula is:

Minimum number of students who solved all four questions =
(Sum of students who solved each question) − (3 × Total students)

Step-by-Step Calculation:
Sum of students who solved each question:
100 + 95 + 90 + 80 = 365

Now subtract (3 × total number of students):
3 × 120 = 360

Now subtract:
365 − 360 = 5

Final Answer:
S. Ans. (b) 5