CAT 2022 Question Paper | Quant Slot 2

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

Video Explanation

Explanatory Answer

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.