CAT 2022 Question Paper | Quant Slot 2

CAT Questions

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 7 : 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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Video Explanation

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Explanatory Answer

Day	Increase	Total
1	-	100
2	\( \frac { 1 } { 2 } \times 100 = 50 \)	150
3	\( \frac { 1 } { 3 } \times 150 = 50 \)	200
4	\( \frac { 1 } { 4 } \times 200 = 50 \)	250
…	…	…

Basically, we see that every day the number of particles increases by 50.
We need to reach 1000 particles from 100 particles on day 1.
Or, we need to increase by 900 particles.
At the rate of 50 particles per day, it takes 18 days to increase by 900 particles.
So on the 19^th day the number of articles will be 1000.

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The answer is '19'

Choice A is the correct answer.

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