Question

In a class containing 120 students, 65 students drink tea and 84 students drink coffee. It x students drink both tea and coffee, what is the value of x ?

• A. 39
• B. 65
• C. $29 \le x \le 65$
• D. $29 \le x \le 84$

Answer 1

Answer: (C)

$29 \le x \le 65$

Answer 2

Let T denote the set of students who drink Tea and C denote the set of students who drink coffee. As given: n (T) = 65, n (C) = 84, Let x denote number of students who take tea and coffee both. n(T $\cup$ C) = 120 and n(T $\cap$ C) = x n(T $\cup$ C) = n(T) + n(C) - n(T $\cap$ C) $\Rightarrow \, 120 \ge 65 + 84 - x$ $x \ge 149 - 120 \ge 29$ and $x \le n (T)$ $\Rightarrow \, x \le 65 \therefore \, 29 \le x \le 65$