How many two-digit numbers are divisible by 3?

30

The correct answer is Option (1) → 30

Step 1: Identify the first and last two-digit numbers divisible by 3

• Smallest two-digit number = 10 → divisible by 3?
  $10 ÷ 3 = 3$ remainder 1 → No → next number 12
• Largest two-digit number = 99 → divisible by 3?
  $99 ÷ 3 = 33$ remainder 0 → Yes

Step 2: Find total numbers

Numbers divisible by 3 form an AP: 12,15,18,...,99

$\text{Number of terms } n = \frac{\text{last term - first term}}{\text{common difference}} + 1$

$n = \frac{99 - 12}{3} + 1 = \frac{87}{3} + 1 = 29 + 1 = 30$