# CAT 2018 Question Paper | Quants Slot 1

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

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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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