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If among 200 students | Quantitative Aptitude - Modern Maths – Set Theory

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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Set Theory: If among 200 students . Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2018 - Slot-1 - Set Theory - Question- 3 - If among 200 students

Q. 3: If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be
1. 93
2. 26
3. 23
4. 96

Correct Answer: 1. 93

Let the number of students who like both pizza and burger be ‘m’ . The number of students who like neither of them be n

 

From venn diagram 105 – m + m + 134 – m + n = 200 m – n = 39

 

∴ The possible values of (m, n) are (39, 0) (40, 1)…….(105, 66)

 

∴ The number of students who like only burger is lies in the range [134 – 105, 134 – 39] = [29, 95]

 

∴ From options, 93 is a possible answer

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