Question

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The values of m and n are, respectively,

• A. 44658
• B. 44746
• C. 44655
• D. 44749

Answer 1

Answer: (B)

44746

Answer 2

$2^{m} - 2^{n} = 112 \Rightarrow 2^{n} \left(2^{m-n }-1\right) = 16 \times 7$ $\therefore\quad2^{n} \left(2^{m-n} -1\right) = 2^{4}\left(2^{3} -1\right)$ Comparing we get $n = 4$ and $m - n = 3$ $\Rightarrow n = 4$ and $m = 7$