Question

Digit sum (DG) is defined as the sum of the digits of a number till you get a single digit number. Eg) DG(40)=4+0=4. DG(345)=DG(12)=DG(3)=3. How many positive integers (n) are there between 500 and 1500 such that DG(N)=7?

• A. 98
• B. 58
• C. 110
• D. 111

Answer 1

The correct option is D

111

Approach 1: Logic
The first number which satisfies this is 502. The next number will be 511 and so on. The terms will fall in an Arithmetic Progression with common difference = 9. Last term = 1492.
Number of terms $=\frac{990}{9}+1=111.$

Approach 2: Shortcut in a Shortcut!
Digit sum of numbers will fall in an Arithmetic Progression with a common difference of 9. Thus, there can be $\frac{1500-500}{9}=111$ or 112 such numbers.
Since only 111 is there in the answer options, you can mark it directly.