Question

There are $3$ electives offered to the students in a class of $92$ ( The students have a choice of not choosing any elective). $60$ students opted for marketing, $80$ for finance and $50$for systems, $40$ students opted for both marketing and systems, $50$ for both marketing and finance and $45$for both finance & systems. What is the maximum number of students who opted for all $3$ electives?

• A. $20$
• B. $30$
• C. $34$
• D. $37$

Answer 1

The correct option is D $37$

Let the number of students who opted for all three electives $=x$.

Then the number of students who opted for both finance and systems $=45-x$.

The number of students who opted for marketing and finance $=50-x$.

The number of students who opted for marketing and systems $=40-x$.

Number of students who opted for marketing alone $=60-(40-x+50-x+x)=x-30$

Number of students who opted for finance alone $=80-(45-x+50-x+x)=x-15$

Number of students who opted for systems alone $=50-(40-x+45-x+x)=x-35$

Now the total number of students who opted for atleast one elective $=x+45-x+50-x+40-x+x-30+x-15+x-35$

$=x+55$.

Now total number of students $=92$.

Maximum value of $x+55$ is $92$. Hence maximum value of $x$ is $92-55=37.$