CAT 2023 Set-3 | Quantitative Aptitude | Question: 7

Question

Let $n$ be any natural number such that $5^{n-1}<3^{n+1}$. Then, the least integer value of $m$ that satisfies $3^{n+1}<2^{n+m}$ for each such $n$, is

Comments

One catch in the question that i liked, for whatever value of $n$ we choose $3^{n+1} <2^{n+m}$ must be satisfied.

I checked for initial values of $n=1,2,3,4$ and i was getting $m$ as $4$, which i assumed was the answer, but I was wrong. for $n=5$ we i got $m=5$ so it is increasing . for $n=6$, $5^{n-1}<3^{n+1}$ is not satisfied , hence we can only take $n=1,2,3,4,5$ for which we must take $m\geq 5$.

Checking on few initial values can be injurious :)