CAT 2018 Slot 2 QA Question & Solution
AlgebraHard
Question
If A = {$6^{2n} -35n - 1$}, where $n$ = 1,2,3,... and B = {35($n$-1)}, where $n$ = 1,2,3,... then which of the following is true?
Options
Every member of A is in B and at least one member of B is not in A
Neither every member of A is in B nor every member of B is in A
Every member of B is in A.
At least one member of A is not in B
Solution
If we carefully observe set A, then we find that $6^{2n} -35n - 1$ is divisible by 35. So, set A contains multiples of 35. However, not all the multiples of 35 are there in set A, for different values of $n$.
For $n = 1$, the value is 0, for $n = 2$, the value is 1225 which is the 35th multiple of 3.
If we observe set B, it consists of all the multiples of 35 including 0.
So, we can say that every member of set A will be in B while every member of set B will not necessarily be in set A.
Hence, option A is the correct answer.