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

The question is from CAT Set theory. It is about factors and multiples of some numbers and their union and intersection. 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 2023. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 1: Set F_n gives all factors of n. Set M_n gives all multiples of n less than 1000. Which of the following statements is/are true?

i. F₁₀₈ ∩ F₈₄ = F₁₂
ii. M₁₂ ∪ M₁₈ = M₃₆
iii. M₁₂ ∩ M₁₈ = M₃₆
iv. M₁₂ ⊂ (M₆ ∩ M₄)

1. i, ii and iii only
2. i, iii and iv only
3. i and iii only
4. All statements are true

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Set theory: This is more a question on Number Systems than on Set Theory.

i. F₁₀₈ ∩ F₈₄
This is the set of all numbers that are factors of both 108 and 84
=> this is set of all common factors of 84 and 108
=> this is set of numbers that are factors of the Highest Common Factor of 84 and 108.
HCF (84, 108) = 12.
F₁₀₈ ∩ F₈₄ = F₁₂ - this is true.

ii. M₁₂ will have numbers {12, 24, 36, 48, ….} Numbers like 12, 24, … will not feature in M₃₆.
So, Statement B cannot be true.

iii. M₁₂ ∩ M₁₈ - this is the set of all common multiples of 12 and 18.
This is the set of numbers that are multiples of the Least Common Multiple of 12 and 18. (which is 36).
This statement is also true.

iv. Using the same logic as that used in statement iii, we can determine that statement iv is also true. Remember that every set is a subset of itself.

The question is "Which of the following statements is/are true?"

Hence, the answer is i, iii and iv are true.

Choice B is the correct answer.