Question

Suppose \(n\) is an integer such that the sum of digits of \(n\) is 2, and \(10^n<n<10^{n+1}\). The number of different values of \(n\) is

• A. 11
• B. 10
• C. 9
• D. 8

Hint:

When dealing with sum of digits problems, list all possible combinations of digits that satisfy the conditions.

Answer 1

The Correct Option is C

The sum of digits of \(n\) is 2, so \(n\) could be any number whose digits sum to 2, and that falls within the range \(10^n<n<10^{n+1}\). After examining all possible cases, the number of such values is 9. \[ \boxed{9} \]