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 or 5 or both?

• A. 100
• B. 150
• C. 3125
• D. 1500
• E. 125

Hint:

Divisible by 2 or 5 → last digit must be 0, 2, or 5. Handle leading-digit restrictions separately when forming valid numbers.

Answer 1

The Correct Option is D

Step 1: Divisibility rule.
A number is divisible by 2 or 5 if its last digit is 0, 2, or 5.

Step 2: Choose last digit.
Options = 3 (0, 2, or 5).

Step 3: Choose first digit.
It cannot be 0 (since 5-digit number). So, 4 choices (2, 3, 4, 5).

Step 4: Choose middle three digits.
Repetition is allowed, so each of the 3 positions has 5 choices.
Thus middle part \(= 5^3 = 125\).

Step 5: Multiply.
Total numbers \(= 4 \times 125 \times 3 = 1500\).

Final Answer:
\[ \boxed{1500} \]