CAT 2025 Slot 3 QA Question 15: In a class of 150 students, 75 students chose physics, 111 students chose mathematics and 40 students chose chemistry. All students chose at least one of the three subjects and at least one student ch

Question

In a class of 150 students, 75 students chose physics, 111 students chose mathematics and 40 students chose chemistry. All students chose at least one of the three subjects and at least one student ch

Accepted Answer

Let the number of students who chose both physics and chemistry be $x$. Then chemistry and mathematics is also $x$, and physics and mathematics is $2x$. Let the number who chose all three be $t$.
Using inclusion-exclusion,
$150 = 75 + 111 + 40 - (2x + x + x) + t$
$150 = 226 - 4x + t$
$4x = 76 + t$
S