What is the sum of ten odd numbers and eleven even numbers? (even/odd)

Answer

To find the sum of ten odd numbers and eleven even numbers and determine whether the result is odd or even, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Odd and Even Numbers**:
- Odd numbers are integers that cannot be divided evenly by 2 (e.g., 1, 3, 5, 7, ...).
- Even numbers are integers that can be divided evenly by 2 (e.g., 0, 2, 4, 6, ...).

2. **Counting the Numbers**:
- We have 10 odd numbers.
- We have 11 even numbers.

3. **Sum of Odd Numbers**:
- The sum of any two odd numbers is always even.
- Therefore, the sum of 10 odd numbers (which can be grouped as pairs) will also be even.
- For example, if we take 1, 3, 5, 7, 9, the sum is 25 (odd), but if we add another odd number, it will still yield an even number when summed with another odd number.

4. **Sum of Even Numbers**:
- The sum of any two even numbers is always even.
- Thus, the sum of 11 even numbers will also be even.

5. **Combining the Sums**:
- Now, we have the sum of 10 odd numbers (which is even) and the sum of 11 even numbers (which is also even).
- When we add an even number to another even number, the result is always even.

6. **Final Calculation**:
- Since both sums are even, the total sum of 10 odd numbers and 11 even numbers will be:
\[ \text{Even (from odd numbers)} + \text{Even (from even numbers)} = \text{Even} \]

### Conclusion:
The sum of ten odd numbers and eleven even numbers is **even**.

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