In this episode of TuesdACT, we are taking a look at the principles of multiplying and adding even and odd numbers using an example from *The Real ACT Prep Guide* that lots of students struggle with.

*Real ACT Prep Guide* Test 4 Question 48 on page 599, we are coming for you!

Check out the video or read below for the explanation and a little lesson on even and odd integers.

If is a positive integer, which of the following expressions must be an odd integer?

F.

G.

H.

J.

K.

Alright, let’s pause and go over principles of adding, subtracting, and multiplying odd and even numbers. Here’s how it shakes out.

Even + Even = Even

Even + Odd = Odd

Odd + Odd = Even

Even x Even = Even

Even x Odd = Even

Odd x Odd = Odd

You don’t need to memorize the rules; if you forget, just go through the examples with easy numbers like 2 and 3 and see what happens. It will be the same for all even and odd numbers.

So, for example:

Even + Even = Even 2 + 2 = 4

Even + Odd = Odd 2 + 3 = 5

Odd + Odd = Even 3 + 3 = 6

Even x Even = Even 2 x 2 = 4

Even x Odd = Even 2 x 3 = 6

Odd x Odd = Odd 3 x 3 = 9

Question 48 is also a great example of how you can find important clues in the answer choices on the ACT. Notice that all of our answer choices have the number 3 in them, so all of our answer choices are doing something with an odd number.

Now let’s test with values for

**Answer Choice F:**

3 is raised to a power of

Since an odd number multiplied by an odd number is always an odd number, and because in this case we are just multiply 3 (an odd number) by itself a number of times, it will always be odd. So F is our answer, but let’s check the rest.

**Answer Choice G:**

**Answer Choice H:**

**Answer Choice J:**

__neither even nor odd__. By rule, the terms even or odd apply only to integers not to fractions.

**Answer Choice K:**

So our answer is F.