How many 4 digit even integers are multiple of 3Solution4 di

How many 4 digit even integers are multiple of 3?

Solution

4 digit even integrs to be multiple of 3, it should also be divisible by 2 (as even) and 3 both. So, to ensure that the number is even and divisible by 3, the number should be divisible by 3 x 2 = 6.

First 4 digit number divisible by 6 is 1002. Last 4 digit number divisible by 6 is 9996.

(9996-1002)/6 = 1499

Including the number 1002, its 1499+1 = 1500

So, total 4 digit +ve even numbers multiple of 3 = 1500

since its 4-digit number are integers, it can be negative number too.

so, total 4-digit even integers multiple of 3 = 1500 x 2 = 3000