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chacha0212
- Junior | Next Rank: 30 Posts
- Posts: 16
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.How many integers are divisible by 3 between 10! and 10!+20 inclusive?
A) 6
B) 7
C) 8
D) 9
E) 10
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.
Answer: B
Cheers,
Brent
