In a class of 100 students, 55 students passed in Mathematics and 67 students passed in Physics. If the number of students who passed in Mathematics only is 22, how many students passed in Physics only?
Answer: D
Let M be the set of students who passed in Mathematics and P be the set of students who passed in Physics.
Given: n(M) = 55, n(P) = 67.
Number of students who passed in Mathematics only is n(M) - n(M ∩ P) = 22.
From this, we can find the number of students who passed in both subjects:
55 - n(M ∩ P) = 22 \(\Rightarrow\) n(M ∩ P) = 55 - 22 = 33.
Now, we can find the number of students who passed in Physics only:
Physics only = n(P) - n(M ∩ P) = 67 - 33 = 34.