# 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 venn diagrams. We just need to draw the diagram without any mistakes to solve this one. 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 19: A factory has 80 workers and 3 machines. Each worker knows to operate atleast 1 machine. If there are 65 persons who knows to operate machine 1, 60 who knows to operate machine 2 and 55 who knows to operate machine 3, what can be the minimum number of persons who knows to operate all the three machines?

1. 15
2. 20
3. 30
4. 40

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##### Method of solving this CAT Question from Set theory: If you get the Venn Diagram right, you are halfway through !!

Let’s start with taking a random value for all three category. So let’s first take 40 for the all three category. Now 65 + 60 + 55 = 180, this means there is an extra count of 180 – 80 = 100.

Now as we know that the extra count occurs in the in the exactly two area and the all three area. So let’s try put the extra count in these area.

Trial 1 - Since 40 is already assumed to be in the all three area, it takes care of extra count of 40 x 2 = 80. Thus we are left with 20 as extra count which we have to place at the exactly two area

Thus in the above case our venn diagram will look as:

A close look in the figure tells us that we can further decrease the value of all the three area. A bit of logical thinking will bring us to the value 20. No value less than 20 can satisfy the conditions of the question. As there is no scope left for reallocating numbers left from one area to another in this case.

Hence the final venn diagram will look as:

The question is "what can be the minimum number of persons who knows to operate all the three machines?"

##### Hence, the answer is "20".

Choice B is the correct answer.

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