CAT 2018 Slot 1 - QUANT Question 20

Question 20

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

Solution

It has been given that among 200 students, 105 like pizza and 134 like burger.
The question asks us to find out the number of students who can be liking only burgers among the given values. 

The least number of students who like only burger will be obtained when everyone who likes pizza likes burger too. 
In this case, 105 students will like pizza and burger and 134-105 = 29 students will like only burger. Therefore, the number of students who like only burger cannot be less than 29.

The maximum number of students who like only burger will be obtained when we try to separate the 2 sets as much as possible. 
There are 200 students in total. 105 of them like pizza. Therefore, the remaining 95 students can like only burger and 134-95 = 39 students can like both pizza and burger. As we can see, the number of students who like burger cannot exceed 95. 

The number of students who like only burger should lie between 29 and 95 (both the values are included). 
93 is the only value among the given options that satisfies this condition and hence, option D is the right answer. 


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