CAT 2020 Slot 2 QA Question 23: Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subje

Question

Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subje

Accepted Answer

Let the number of students choosing only Chemistry and Mathematics be $a$, only Mathematics and Physics be $b$, and only Chemistry and Physics be $c$. The number choosing all three is $18$.

Since $23$ students choose Mathematics,
$a + b + 18 = 23$
$a + b = 5$

Since $25$ students choose Physics,
$b