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

###### CAT Questions | Set theory | Number Of Elements CAT Questions

The question is from CAT Set theory. It combines the set theory with number theory. Our task is to find out the number of elements in all three sets. 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 2019. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 6: Set P comprises all multiples of 4 less than 500. Set Q comprises all odd multiples of 7 less than 500, Set R comprises all multiples of 6 less than 500. How many elements are present in P ∪ Q ∪ R?

1. 202
2. 243
3. 228
4. 186

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### Explanatory Answer

##### Method of solving this CAT Question from Set theory: Does union represents OR or AND?

This question involves both Number Systems and Set Theory.
Set P = {4, 8, 12, ….496} ↦ 124 elements {all elements from 1 * 4 to 124 * 4}
Set Q = {7, 21, 35, 49,……497} ↦ {7 * 1, 7 * 3, 7 * 5, ….. 7 * 71} ↦ 36 elements.
Set R = {6, 12, 18, 24, …..498} ↦ {6 * 1, 6 * 2, 6 * 3, ….. 6 * 83} ↦ 83 elements.

Sets P and R have only even numbers; set Q has only odd numbers. So,
P ∩ Q = Null set
Q ∩ R = Null set
P ∩ Q ∩ R = Null set
So, If we find P ∩ R , we can plug into the formula and get P ∪ Q ∪ R

P ∩ R = Set of all multiples of 12 less than 500 = {12, 24, 36,…..492}
= {12 * 1, 12 * 2 , 12 * 3, …12 * 41} ↦ This has 41 elements
P ∪ Q ∪ R = P + Q + R – (P ∩ Q) – ( Q ∩ R) – (R ∩ P) + (P ∩ Q ∩ R)
P ∪ Q ∪ R = 124 + 36 + 83 – 0 – 0 – 41 + 0 = 202

The question is "How many elements are present in P ∪ Q ∪ R?"

##### Hence, the answer is "202".

Choice A is the correct answer.

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