[email protected] wrote:How many numbers from 10! to 10!+20
inclusive, are divisible by 3?
NOTE: I reworded the question to avoid ambiguity.
There's a nice rule that says:
If M is divisible by k, and N is divisible by k, then (M + N) is divisible by k.
First, since 10! = (10)(9)(8)..(
3)(2)(1), we know that 10! is divisible by 3.
So, by the
above rule, we know that 10! + 3 is divisible by 3
And 10! + 6 is divisible by 3
10! + 9 is divisible by 3
10! + 12 is divisible by 3
10! + 15 is divisible by 3
10! + 18 is divisible by 3
So, there are 7 integers from 10! to 10! + 20 inclusive that are divisible by 3.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
