CAT 2023 Surds and Indices Question (Hard)

Question

Let and be two positive integers such that there are exactly 41 integers greater than and less than , which can be expressed as powers of 2 . Then, the smallest possible value of is

Accepted Answer

Step 1 We need 41 powers of between and Note , So we need 41 integers between and Total powers of between and exclusive Set Step 2 Minimize with Let Minimized when So, Final Answer

CAT 2023

Quantitative

Surds and Indices

Hard

Let $n$ and $m$ be two positive integers such that there are exactly 41 integers greater than $8^m$ and less than $8^n$ , which can be expressed as powers of 2 . Then, the smallest possible value of $n+m$ is

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