Question

Assume x and y are two odd numbers and x/y is an integer. which of the following statements are true?

Answer 1

Answer:

2. xy is odd

Step-by-step explanation:

We can represent the two odd numbers as 2a + 1(x) and 2b + 1(y).

1. x + y is odd

We can add x + y:

2a + 1 + 2b + 1

2a + 2b + 2

From this, we can factor out 2:

2(a + b + 2)

Since 2 is a factor, the number x + y cannot be odd.

2. xy is odd:

We can multiply x and y:

(2a + 1)(2b + 1)

4ab + 2a + 2b + 1

From the first three terms, we can factor out 2:

2(2ab + a + b) + 1

We can say that 2(2ab + a + b) is an even number because it has a factor of 2. We are adding one to it, and one added to any even number is odd, so xy is odd.

We do not need to calculate further because we have already found an answer.