Question 298966
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The maximum sum of digits of a three-digit number is obviously
the sum of the digits of 999 which is 9+9+9 or 27, a two-digit
number, the sum of whose digits is 9.  All two-digit numbers
between 20 and 26 have sum of digits less than 9.  So we look
at the two-digit numbers less than 20 and see if any have sum
of digits greater than 9.  We quickly find that 19 has the 
maximum sum of digits (1+9=10) of all integers less than 27.
So the three digit numbers with maximum sum of digits of sums 
of digits are those whose digits have sum 19.  There are many 
three-digit numbers with sum of digits 19, such as 199,
595, 649, 991, 829, 577, etc. etc.  

So the answer is 10, choice B.

Edwin</pre>