Let n and m be two positive integers such that there are exactly 41 integers greater than 8m and less than 8n, which can be expressed as powers of 2. Then, the smallest possible value of n + m is?
Explanation:
8m = 23m and 8n = 23n
Now, 23m < 2x < 23n
We have to find least possible value of (m + n) such that there are 41 possible values of x.
Least possible of m = 1, hence we get, 23 < 2x < 23n
Now, x can be any interger from 4 till 44 (41 values).
∴ Least possible value of 3n = 45, hence n = 15.
∴ Least possible value of m + n = 1 + 15 = 16.
Hence, option (c).
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