Question

Out of 400 students who attended a seminar, 240 opted for written exam, 200 opted for presentations, 160 opted for assignments and 20 did not opt for giving any of the three methods of test. 200 students had exactly one of the three methods of test. How many students opted for exactly two of the three testing methods?

Accepted Answer

A. Total appeared = $400 - 20 = 380$. Let $E_1, E_2, E_3$ be students with 1, 2, 3 methods. $E_1 + E_2 + E_3 = 380$. Given $E_1 = 200 \Rightarrow E_2 + E_3 = 180 \quad 	ext{--- (i)}$. Total opts = $240 + 200 + 160 = 600$. $E_1 + 2E_2 + 3E_3 = 600 \Rightarrow 200 + 2E_2 + 3E_3 = 600 \Rightarrow 2E_2 + 3E_3 = 400 \quad 	ext{--- (ii)}$. Multiply (i) by 2: $2E_2 + 2E_3 = 360$. Subtracting gives $E_3 = 40$. $E_2 = 180 - 40 = 140$.

3-Set Venn Diagram Seminar Test Methods

Explanation

Practise this under exam conditions