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Question :
Let nn and mm be two positive integers such that there are exactly 41 integers greater than 8m8m and less than 8n8n, which can be expressed as powers of 2. Then, the smallest possible value of n +mn + m is
Started 1 month ago by Shashank in
Option C
is the correct answer.
Explanatory Answer
We need to have 41 integers that can be expressed as powers of 2 between 8m and 8n.
That is we need to have 41 integers that can be expressed as powers of 2 between 23m and 23n.
The numbers will be of the form: 23m,23n+1,23m+2,23m+3,…,23m+41,23n
clearly, 3n−1=3m+41
3(n−m)=42
n−m=14
The smallest value m
can take =1
, then n=15
m+n=1+15=16
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