I am less than 500. I am divisible by 11 and 5. I have three digits. The sum of my digits is 14

Answer 1

275

Answer 2

To be divisible by both 11 and 5, the number must be a multiple of 55
those are: 55, 110, 165, 220, 275, ..
ahh, 275 has its digits add up to 14

For questions in the area of "pure" math such as this question, for me the method of obtaining the answer was more important than the answer itself.