# CAT Quantitative Aptitude Questions | CAT Set theory Questions - Union and Intersection

###### CAT Questions | Set theory | Union and Intersection
CAT Questions

The question is from CAT Set theory. It is about union and intersection. We just need to form the equation after assuming x. CAT exam is known to test on basics rather than high funda ideas. CAT also tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2020. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 17: In Grand Oberoi hotel, 1160 guests are present currently. The hotel provides the following extra facilities: Gym, Swimming, Fun park, Food. During a regular survey the management team of Oberoi noticed something quite extraordinary about the extra facilities provided by them. They noticed that for every person who uses ‘F’ no. of facilities, there are exactly 3 persons who uses at least (F-1) no. of facilities, F = 2, 3, 4. They also found that the no. of persons who used no extra facilities is twice the no of person that used all the 4 facilities. Help the management team to find out how many persons used exactly 3 facilities.

1. 40
2. 60
3. 80
4. 100

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##### Method of solving this CAT Question from Set theory: Relating atleast 'n' and exactly 'n'!

Since, for every person who uses ‘F’ no of facilities, there are exactly 3 person who uses atleast (F-1) no. of facilities. If we take the no. of persons who uses all the four facilities to be ‘x’ then the no. of person who uses atleast 3 facilities will be 3x and so on.

The No. of persons who use exactly 3 facilities = 3x – x = 2x
Thus, the no. of persons who opt for various facilities can be summarized as follows:

n    number of person who uses atleast n facilities   number of person who uses exactly in facilities
4 x x
3 3x 2x
2 9x 6x
1 27x 18x

We also know that no of person who uses no facilities = twice of those who uses all the 4 facilities = 2x.
So according the above deductions we can clearly see that the number of person the hotel would be
x + 2x + 6x + 18x + 2x = 29 x = 1160
x = 40
Hence the number of person who uses exactly three science = 2x = 80

The question is "Help the management team to find out how many persons used exactly 3 facilities."

##### Hence, the answer is "80".

Choice C is the correct answer.

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