CAT 2022 Progression Question (Hard)

Question

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

Accepted Answer

Step 1 Initial particles on Day 1 100 For each day n 2 Each particle creates 1 new particle for every n particles New particles floor of total n Simulate day by day until total reaches 1000. Let s define - Day 1 total 100 Step 2 Iterate Day 2 100 2 50 total 150 Day 3 150 3 50 total 200 Day 4 200 4 5

CAT 2022

Quantitative

Progression

Hard

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

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