Find the sum of all odd numbers of 4 digits which are divisible by 9.?

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Sum of all odd numbers of 4 digits divisible by 9

To find the sum of all odd numbers of 4 digits that are divisible by 9, we need to follow a systematic approach. Let's break it down into steps:

Step 1: Identify the range
We are looking for 4-digit numbers, so the range of numbers to consider is from 1000 to 9999.

Step 2: Identify the divisible numbers
To find the numbers divisible by 9, we need to check if the sum of their digits is divisible by 9.

Step 3: Find the odd numbers
Out of the divisible numbers, we need to identify the odd ones. Odd numbers are those that leave a remainder of 1 when divided by 2.

Step 4: Calculate the sum
Finally, we need to sum up all the odd numbers obtained in the previous step.

Let's calculate the sum of all odd 4-digit numbers divisible by 9:

1. Range: 1000 to 9999

2. Divisible Numbers:
- We need to find the numbers whose sum of digits is divisible by 9.
- We can start by checking the first number, 1000.
- The sum of its digits is 1 + 0 + 0 + 0 = 1, which is not divisible by 9.
- Moving on to the next number, 1001.
- The sum of its digits is 1 + 0 + 0 + 1 = 2, which is also not divisible by 9.
- We continue this process for all numbers in the range until we reach a divisible number.

3. Odd Numbers:
- Out of the divisible numbers, we need to identify the odd ones.
- For example, if we find a number like 1080 that is divisible by 9, we need to check if it is odd.
- 1080 is not odd because it is divisible by 2.
- We continue this process until we have a list of odd numbers.

4. Sum Calculation:
- Once we have the list of odd numbers, we can calculate their sum.
- We add up all the odd numbers obtained in the previous step.

5. Final Answer:
- The sum of all odd 4-digit numbers divisible by 9 is the result obtained from step 4.

By following these steps, we can find the sum of all odd 4-digit numbers that are divisible by 9.

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