Find the sum of the greatest 4-digit number divisible by 6 and the smallest 4-digit number divisible by 3.

Step 1: Find the greatest 4-digit number divisible by 6
The largest 4-digit number overall is 9999.
Dividing 9999 by 6:

9999=6×1666+3
Subtracting the remainder from 9999:

9999−3=9996
Thus, the greatest 4-digit number divisible by 6 is 9996.

Step 2: Find the smallest 4-digit number divisible by 3
The smallest 4-digit number overall is 1000.
Let's check the sum of digits of 1000, which is 1. For a number to be divisible by 3, the sum of digits must be a multiple of 3. The next closest integer where the sum of digits is a multiple of 3 is 1002 (1+0+0+2=3).
Thus, the smallest 4-digit number divisible by 3 is 1002.

Step 3: Calculate the required sum

Sum=9996+1002=11004