Mathematics · Sets and Relations

JEE Main 2024 — 4 April, Shift 1 — Question 22

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let m and n respectively be the least and the most number of students who studied all the three subjects. Then $\mathrm{m}+\mathrm{n}$ is equal to $\qquad$

Answer: 45

Numerical answer — enter this value.

Step-by-step solution

$125 \leq \mathrm{m}+90-\mathrm{x} \leq 130$

$85 \leq \mathrm{P}+70-\mathrm{x} \leq 95$

$75 \leq \mathrm{C}+80-\mathrm{x} \leq 90$

$\mathrm{m}+\mathrm{P}+\mathrm{C}+120-2 \mathrm{x}=210$ $

$\Rightarrow 15 \leq \mathrm{x} \leq 45 \& 30-\mathrm{x} \geq 0$

$\Rightarrow 15 \leq \mathrm{x} \leq 30$

$30+15=45$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Mathematics
Chapter: Sets and Relations
Topic: Sets