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If A = {6^2n -35n -1: n = 1,2,3,…} | Quantitative Aptitude - Modern Maths – Set Theory

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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Set Theory: If A = {6^2n -35n -1: n = 1,2,3,…} . Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2018 - Slot-2 - Arithmetic - Question-4 - If A = {6^2n -35n -1: n = 1,2,3,…}

Q. 4: If A = {6^2n -35n -1: n = 1,2,3,…} and B = {35(n-1) : n = 1,2,3,…} then which of the following is true?
1. Neither every member of A is in B nor every member of B is in A
2. Every member of A is in B and at least one member of B is not in A
3. Every member of B is in A.
4.  At least one member of A is not in B

Given, A = 36^n – 35n – 1 = 36^n – 1^n – 35n

Since a^n – b^n is divisible by a – b for all positive integral values of n, So A is a

multiple of 35 for any integral value of n and B is a set containing all the

multiple of 35 including 0.

Hence, every member of A is in B but not every element of B is in A.

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