CAT 2022 Slot 2 QA Q13 Number Systems

Question 13 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

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

A
5
B
7
C
4
D
6

Answer: (B) 7 Number Systems MCQ

Solution

\(k!\) divides \(15000!\) exactly when \(k\le15000\).
So we need \(n!\le15000\): \(7!=5040\) works, \(8!=40320\) does not. Largest \(n=7\).