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

$n$

From CAT Score to IIM Selection!

Practice

Features

Support

CAT 2023

Quantitative

Surds and Indices

Hard

Let nnn and mmm be two positive integers such that there are exactly 41 integers greater than 8m8^m8m and less than 8n8^n8n , which can be expressed as powers of 2 . Then, the smallest possible value of n+mn+mn+m is

From CAT Score to IIM Selection!

$n$