Question

The total number of natural numbers that lie between 10 and 300 and are divisible by 9 is

• A. 32
• B. 30
• C. 33
• D. 34

Hint:

Count multiples of 9 up to 300, subtract those up to 10: floor(300/9) - floor(10/9) = 33 - 1 = 32.

Answer 1

The Correct Option is A

A quick way to count multiples of 9 in a range is to count multiples up to each endpoint and subtract.

1. Number of multiples of 9 from 1 to 300: $\lfloor 300/9 \rfloor = 33$ (since $9 \times 33 = 297 \le 300$).
2. Number of multiples of 9 from 1 to 10: $\lfloor 10/9 \rfloor = 1$ (just the number 9 itself, which is not between 10 and 300 anyway).
3. Multiples of 9 strictly between 10 and 300 $= 33 - 1 = 32$.

This matches the AP-based count exactly.

So the correct answer is option A, 32.