CAT 2018 Question Paper | Quants Slot 2
CAT Previous Year Paper | CAT Set Theory Questions | Question 32
CAT Questions There were some questions in the CAT 2018 Question paper which the test takers might want to side-step. This question from Set Theory can be regarded as something of that sort. Nevertheless, if you are a master at solving highly-complex CAT Algebra questions, this might not be as intimidating as it looks. Try this and have a look at the explaination for this question from CAT Previous Year Paper 2018.
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?
- Neither every member of A is in B nor every member of B is in A
- Every member of A is in B and at least one member of B is not in A
- Every member of B is in A.
- At least one member of A is not in B
Every member of A is in B and at least one member of B is not in A
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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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