Question

Which conjecture, if any, could be made about the sum of two even integers and one odd integer?

The sum will be an even integer.
The sum will be negative.
It is not possible to make a conjective.
The sum will be an odd integer.

Answer 1

The sum will be an odd integer

Explanation:

The even integers are divisible by 2 (as they are even) so we can write them as 2 times integer like this.

First even number = 2x

Second even number = 2y

An odd number is not divible by 2, but the number 1 smaller is even, so

The odd number = 2z + 1

Let's add them

2x + 2y + 2z + 1 = 2(x+y+z) + 1

So our sum is 1 more than another even number, so the sum is an odd number.

Answer 2

The conjecture that the sum will be an odd integer is supported by these examples and holds true in general.

The conjecture that can be made about the sum of two even integers and one odd integer is that the sum will be an odd integer.

To understand why this conjecture is true, let's consider some examples.

Let's say we have two even integers, such as 2 and 4, and one odd integer, such as 3. When we add these numbers together (2 + 4 + 3), we get a sum of 9, which is an odd integer.

Similarly, if we have two other even integers, such as 6 and 8, and another odd integer, such as 5, the sum (6 + 8 + 5) will be 19, which is also an odd integer.

From these examples, we can see that regardless of the specific even and odd integers chosen, the sum of two even integers and one odd integer will always be an odd integer.