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CAT Previous Year Paper | CAT Set Theory Questions | Question 32

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Question 32 : If A = {62n - 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

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Explanatory Answer

Method of solving this CAT Question from Set Theory

Given that A = {62n - 35n - 1 : n = 1 , 2 , 3 , ...} and B = {35(n-1) : n = 1 , 2 , 3 , ...}
A = {62n - 35n - 1}
When n = 1
{62 - 35 - 1} = 0
when n = 2
{64 - 35(2) - 1} = 1225
when n = 3
{66 - 35(3) - 1} = 46550
B = {35(n-1) : n = 1 , 2 , 3 , ...}
When n = 1
{35(0)} = 0
when n = 2
{35(1)} = 35
when n = 3
{35(2)} = 70
So B is more predictable here since it has every multiple of 35 ie. {0 , 35 , 70 , 10 , 140 , .......}
From this we can see that A is a subset of B ie. Every element of A is in B and not the vice versa
Therefore every member of A is in B and at least one member of B is not in A

The question is "If A = {62n - 35n - 1: n = 1,2,3,...} and B = {35(n-1) : n = 1,2,3,...} then which of the following is true?"

Hence, the answer is Every member of A is in B and at least one member of B is not in A

Choice B is the correct answer

 

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