There are 90 three-digit odd numbers that are divisible by 5.
Here's how we determine that:
- Understanding the Requirements: We need to find 3-digit numbers that are both odd and divisible by 5. This means the numbers must:
- Be between 100 and 999 (inclusive).
- End in either 0 or 5 (divisibility rule for 5).
- End in an odd digit (odd number requirement).
- Combining the Rules: Given the above requirements, we know that all such numbers must end in '5'.
- Constructing the Numbers:
- The first digit can be any number from 1 to 9 (9 possibilities).
- The second digit can be any number from 0 to 9 (10 possibilities).
- The third digit must be 5 (1 possibility).
- Calculation: To find the total number of such numbers, we multiply the number of possibilities for each digit: 9 10 1 = 90.
Example:
Let’s look at a small range of odd numbers divisible by 5 to understand the pattern:
- 105
- 115
- 125
- ...
- 985
- 995
Reference Information:
The provided reference states, "∴ The required number of 3-digit numbers=12+9=21". This information is not directly relevant to our question, as it appears to be solving a different, unrelated problem. The provided reference likely comes from a separate context.
Therefore, based on the logical analysis of the question requirements, the correct answer is 90.
