CAT 2022 Slot 2 QA Q7 Progressions & Series

Question 7 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

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
  1. A
    19
  2. B
    16
  3. C
    17
  4. D
    18

Answer: (A) 19 Progressions & Series MCQ

Solution

  1. On day \(n\) the count is multiplied by \(1+\frac1n=\frac{n+1}{n}\).
  2. The product telescopes: on day \(m\) the count is \(100\cdot\frac32\cdot\frac43\cdots\frac{m+1}{m}=100\cdot\frac{m+1}{2}\).
  3. \(50(m+1)=1000\Rightarrow m=19\).

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