Question

Each student in a class of $40$, studies at least one of the subjects English, Mathematics and Economics. $16$ study English, $22$ Economics and $26$ Mathematics, $5$ study English and Economics, $14$ Mathematics and Economics and $2$ study all the three subjects. The number of students who study English and Mathematics but not Economics is

• A. $7$
• B. $5$
• C. $10$
• D. $4$

Answer 1

The correct option is B

$5$

Finding the number of students who study English and Mathematics but not Economics:

Given, the total number of students in a class is $40$.

Let, the number of students who study English and Mathematics but not Economics is $x$.

Therefore, from the Venn diagram, we get:

$\begin{array}{rcl}11-x+3+2+x+12-x+12+5& =& 40\end{array}$

$\Rightarrow$ $\begin{array}{rcl}45-x& =& 40\end{array}$

$\Rightarrow$ $\begin{array}{rcl}x& =& 5\end{array}$

$\therefore$$\mathbf{5}$ students study English and Mathematics but not Economics.

Hence, Option (B) is the correct answer.