sarthakaggarwal
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 subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is
A 22
B 19
C 20
D 21
E 23
Two kinds of students:
Those who took all 3 subjects - These are 18
Those who took exactly 2 subjects -
25 students have Math. Their second subject could be Physics or Chemistry.
But 23 students have Physics. This means 2 of the 25 students will certainly need to take Chemistry. This is the minimum number of students among two subject students who have Chemistry.
It is certainly possible that among those with 2 subjects, there are many more who have Chemistry.
For example, of the 25 who have Math, 10 could have Chemistry and 15 could have Physics. So of 23 who have Physics, 15 already have Math and 8 will have Chemistry. So 18 total have chemistry.
Since we are looking for the minimum number, we get 18 + 2 = 20 have Chemistry