What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15

-- If the number is divisible by 15, then it's divisible by 5 .
So it must end in 5 .
Since it's palindromic, it must also begin with 5 .

Once I reached that point, my brain was worn out from the strain,
so I did the rest of it the cheap and easy way. 

I took my calculator, started at 6,000 (a multiple of 15), and kept
subtracting 15 at a time until I saw a palindromic number.

The first one I saw is  5775 .  So that's the largest 4-digit
palindromic multiple of 15.

The sum of its digits is  (5 + 7 + 7 + 5) = (12 + 12)  =  24 .