# CAT 2022 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 13

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 13 : For some natural number $n$, assume that $(15,000)$ ! is divisible by $(n !) !$. The largest possible value of $n$ is

1. 5
2. 7
3. 4
4. 6

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Let n! = k
We intend to find k such that k! divides 15,000!.
This means, $k $leq 15,000$. $n ! $leq 15,000$ 5! = 120 6! = 120 * 6 = 720 7! = 720 * 7 = 5,040 8! = 5040 * 8 = 40,320 So, the largest value of n such that, $n ! \leq 15,000$ is 7. The question is " For some natural number $n$, assume that $$15,000$$ ! is divisible by $(n !) !$. The largest possible value of $n$ is "

##### Hence, the answer is '7'

Choice B is the correct answer.

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