Question

In a survey of 500 students in a school, 150 students selected in the NDA exam, 200 students selected in the Group X exam and 100 were selected for both Exams. Find how many students were selecing neither NDA exam nor Group X exam.
1. 240
2. 270
3. 260
4. 250

Answer 1

Correct Answer - Option 4 : 250

Concept:

n(A ∪ B)′ = n (U) – n(A ∪ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Calculation:

Let U denote the set of surveyed students

A denote the set of students whose selected in NDA exam 

B denote the set of students whose selected in Group X exam 

Then n(U) = 400, n(A) = 100, n(B) = 150 and n(A ∩ B) = 75.

Now, n(A′ ∩ B′) = n(A ∪ B)′  

⇒ n(A ∪ B)′ = n (U) – n(A ∪ B)

⇒ n(U) – n(A) – n(B) + n(A ∩ B)                        [∵ n(A ∪ B) = n(A) + n(B) - n(A ∩ B)]

⇒ 500 – 150 – 200 + 100  

⇒ 250