An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible?

EXPLANATION

Correct Option (3)

For an integer to be divisible by 3, the sum of its digits must be divisible by 3. The given 8-digit number is 4252746B.

The sum of the digits is calculated as: 4 + 2 + 5 + 2 + 7 + 4 + 6 + B = 30 + B.

For the number to be divisible by 3, the sum of its digits (30 + B) must be divisible by 3. This can be represented as $\frac{30 + B}{3}$ .

Since 30 is already divisible by 3, for the entire sum (30 + B) to be divisible by 3, the digit B must also be divisible by 3.

Considering B as a single digit (0, 1, 2, ..., 9), the possible values for B that are divisible by 3 are 0, 3, 6, and 9.

Thus, there are 4 possible values for B.

Incorrect Options:

Options 1, 2, and 4 are incorrect. The application of the divisibility rule for 3 demonstrates that there are exactly 4 single-digit values for B (0, 3, 6, 9) that make the number 4252746B divisible by 3. Therefore, any other count (2, 3, or 6) does not align with the derived solution.