Question

Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m.n is ___

Answer 1

Correct answer is 28 

Explaination:

No. of subsets of A=2m
No. of subsets of B=2n
2^m=2ⁿ+112
2^m−2ⁿ=112

2ⁿ(2^m−n−1)=112
2ⁿ(2^m−n−1)=2⁴(2³−1)
n=4
m−n=3
m−4=3
⇒m=7
m×n=28
=28