# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Set Theory Questions | Question 22

In CAT 2018 we saw some really challenging problem that gave emphasis to the very basics and the ability of students to comprehend the concepts more than remembering gazillion formulae and shortcuts. This question from Set theory is one such problem. To acclimatize yourself to solve questions of this kind, CAT Previous Year paper is the best place to start off your CAT online preparation. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, visit2IIM's CAT Question Bank

Question 22 :Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is [TITA]

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##### Method of solving this CAT Question from Set Theory

Let us draw a Three set Venn diagram from values given
Since its given that n(H) = n(E) and n(only P) = 0
a + b + 20 + 10 = c + d + 20 + 10
a + b = c + d
As N = 74, a + b + 20 + 10 + c + d = 74
2(a + b) = 44 => a + b = 22
n(H) = a + b + 20 + 10 = 22 + 20 +10 = 52 students

The question is "Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is [TITA]"

##### Hence, the answer is 52 students

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