Question

How many five-digit numbers can be formed using the digits 0, 2, 3, 4 and 5, when repetition is allowed, such that the number formed is divisible by 2 and 5?

• A. 100
• B. 150
• C. 3125
• D. 500
• E. 125

Hint:

For divisibility by 2 and 5 simultaneously, the number must end in 0.

Answer 1

The Correct Option is D

Step 1: Condition for divisibility by 2 and 5.
Number must end in 0.
Step 2: Leading digit cannot be 0.
Choices for first digit = 4 (2,3,4,5).
Step 3: Middle 3 digits.
Each has 5 options (repetition allowed). So total = \(5^3 = 125\).
Step 4: Multiply.
Total numbers = \(4 \times 125 \times 1 = 500\).
Final Answer:
\[ \boxed{500} \]