CAT 2022 Slot 2 Paper

Question : 59 of 66

Marks: +1, -0

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

Solution:

To find the largest possible value of

n

, we need to find the value of

n

such that

n!

is less than

15000

7 !=5040

8 !=40320>15000

This implies

15000 !

is not divisible by

40320 !

Therefore, maximum value

{n}

can take is

7

.
The answer is option B.

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