CAT 2022 Slot 2 QA Question 9: On day one, there are 100 particles in a laboratory experiment. On day $n$, where $n \geq 2$, one out of every $n$ particles produces another particle. If the total number of particles in the laborato

Question

On day one, there are 100 particles in a laboratory experiment. On day $n$, where $n \geq 2$, one out of every $n$ particles produces another particle. If the total number of particles in the laborato

Accepted Answer

On day $n$, one out of every $n$ particles produces one more particle. So, the number of particles is multiplied by:

$1 + \dfrac{1}{n} = \dfrac{n + 1}{n}$

Starting with 100 particles on day 1, the number of particles on day $m$ is:

$100 	imes \dfrac{3}{2} 	imes \dfrac{4}{3} 	imes \dfrac{5}{4}

On day one, there are 100 particles in a laboratory experiment. On day nnn, where n≥2n \geq 2n≥2, one out of every nnn particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day mmm, then mmm equals

On day one, there are 100 particles in a laboratory experiment. On day $n$ , where $n \geq 2$ , one out of every $n$ particles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day $m$ , then $m$ equals