CAT 2022 Slot 2 QA Question & Solution
Question
On day one, there are 100 particles in a laboratory experiment. On day n, where $n\ge2$, one out of every n articles produces another particle. If the total number of particles in the laboratory experiment increases to 1000 on day m, then m equals
Options
Solution
Given, the number of particles on day 1 = 100
On day 2, one out of every 2 articles produces another particle.
The number of particles on day 2 will be $\frac{100}{2}$, i.e. 50 particles
On day 3, one out of every 3 articles produces another particle.
The number of particles on day 3 will be $\frac{100+50}{3}$, i.e. 50 particles
On day 4, one out of every 4 articles produces another particle.
The number of particles on day 4 will be $\frac{100+50+50}{4}$, i.e. 50 particles
Series will be 100, 50, 50, 50,....
It is given,
100 + (m-1)50 = 1000
m = 19
The answer is option A.