# CAT 2018 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Set Theory Questions | Question 32

Solving questions from CAT Previous Year Paper is one of the best ways for CAT Preparation Online. This is a tricky question even though looks easier. You can expect at least one question from Set Theory in your CAT Exam. So it is imperative that you should have a strong foundation in this topic

Question 32 :If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be

1. 26
2. 23
3. 96
4. 93

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

Given that out of 200 students, 105 like Pizza and 134 like Burger
In order to find the possible number of students who like only Burger, we need to find the range between the minimum and maximum possible number of students

Minimum possible number of Students who like only Burger:

For this, we must try to optimize the Venn diagram in such a way that it has maximum intersection
No of Students who like only Burger = 134 – 105= 29

Maximum possible number of Students who like only Burger:

For this, we must optimize the Venn diagram in such a way that it has minimum intersection
We know that total number of Students = 200
So, Minimum number of students who like both = 105 + 134 – 200 = 39 students
Students who like Burger = 134
Max. no of Students who like only Burger = 134 – 39 = 95
So range => 29 ≤ n ≤ 95
From the options, only (D) 93 lies within range

The question is "If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be"

##### Hence, the answer is 93 students

Choice D is the correct answer.

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