Question

How many two-digit numbers are divisible by 3?

• A. 25
• B. 28
• C. 30
• D. 36

Hint:

For problems like this, use the formula for the \(n\)-th term of an arithmetic sequence to find the number of terms divisible by a number.

Answer 1

The Correct Option is C

The smallest two-digit number divisible by 3 is 12, and the largest is 99. The numbers divisible by 3 form an arithmetic sequence: \[ 12, 15, 18, \dots, 99 \] The first term \(a = 12\), the common difference \(d = 3\), and the last term is 99. Using the formula for the \(n\)-th term of an A.P.: \[ T_n = a + (n - 1) \times d \] Substituting the known values: \[ 99 = 12 + (n - 1) \times 3 \] \[ 87 = (n - 1) \times 3 \] \[ n - 1 = 29 \quad \Rightarrow \quad n = 30 \] Thus, there are 30 two-digit numbers divisible by 3.