CAT 2022 Number System Question (Hard)

Question

For some natural number , assume that ! is divisible by . The largest possible value of is

Accepted Answer

Strategy We are to find the largest such that n! leq 15000 Because after that point, will no longer be within , since contains factors up to , and that should not exceed . --- Step-by-Step We want to find the largest such that n! leq 15000 Compute factorials step by step Notice Thus, is the largest

CAT 2022

Quantitative

Number System

Hard

$n$

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CAT 2022

Quantitative

Number System

Hard

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

Master Your PI Skills for Top B-Schools!

$n$