D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the…
D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D?
0
7
8
9
Solution
To minimize the ratio of a 3-digit number to its digit sum, we want a small number with a large digit sum. The number 199 gives ratio $199/19 \approx 10.47$, which minimizes the ratio among 3-digit numbers. The hundred's digit is 1 and the unit's digit is 9, so the difference is $9 - 1 = 8$.