I need to understand the solution.

A

Step-by-step explanation:

Rules:

odd x odd = odd

even x even = even

even x odd = even

even + even = even

odd + odd = even

odd + even = odd

We can determine whether 2a + 3b is odd if we have both statements because we know that a is odd and 2 is even, which means their product will be even. 3 is odd and b is odd, so their product will be odd. The sum of the even and odd will be odd.

If we have just the second statement we can determine the answer because anything multiplied by 2 is even.

So whether or not we know if a is odd, we know that 2a is even because 2 doubles everything which means it's divisible by 2 which means it's even.

However, statement 1 alone is not enough because if a is odd, then 2a is even. However, 3b can be even or odd depending on b. If b is odd, then 3b is odd. if b is even, 3b is even.

Therefore, if you have statement 2 you can answer the question but if you only have statement 1 then you also need statement 2