Mastering TEAS ATI Mathematics: Understanding Even and Odd Integer Products

Two even integers and one odd integer are multiplied together. Which of the following could be their product?

• A. 3.75
• B. 9
• C. 16.2
• D. 24

Answer: (D)

When multiplying two even integers and one odd integer, the product will always be an even integer. This is because the product of any even integer with any other integer (whether even or odd) will always yield an even result. Let's analyze what happens with the potential products mentioned. The first option, 3.75, is a decimal and not an integer, hence cannot be the product of any integers. The second option, 9, is an odd integer. The product of two even integers with one odd integer cannot yield an odd result, therefore this cannot be a valid product. The third option, 16.2, is also a decimal and not an integer, disqualifying it as a valid product as well. The last choice, 24, is an even integer, which aligns perfectly with the necessary criteria for the product of two even integers and one odd integer. Thus, the only product that fits these requirements is 24.

When it comes to preparing for the TEAS ATI Mathematics Test, understanding the properties of integers can truly help demystify some of the trickier questions you might face. For instance, let’s take a closer look at a situation involving two even integers and one odd integer. You might be wondering, “What’s the deal with their product?” Well, if you want to ace those math questions, getting familiar with the ins and outs of integer multiplication is crucial.

Here's the scenario: If you multiply two even integers and one odd integer together, what can we expect for their product? It’ll definitely be an even integer! You know why? The product of any even integer with any other integer—whether even or odd—will always yield an even result. So, let’s break this down, shall we?

Consider the options below for potential products of two even integers and one odd integer:

A. 3.75

B. 9

C. 16.2

D. 24

Now, let’s analyze each one. First up is 3.75. This is a decimal—not an integer—which immediately disqualifies it from being a product of any integers. Next, we have 9. Here’s a fun fact: 9 is an odd integer. Because we're multiplying two even integers with one odd integer, this can’t yield an odd result. So, bye-bye to 9!

Moving on to 16.2—another decimal and thus, like 3.75, cannot belong in our list of integer products. If your math feels challenged by these decimals, remember that they just don’t fit our criteria for integer multiplication.

Finally, we land on 24. This gem is an even integer, fitting perfectly with the specifications of our multiplication. You see, two even integers multiplied together, regardless of the third integer being odd, will always give you an even product. So in this case, 24 is our golden ticket!

Understanding the vital concept that the product of two even numbers, combined with an odd number, results in an even outcome is a fundamental part that every TEAS test-taker should grasp. Think of it as building a solid foundation for your mathematical skills.

Why’s this important? Well, when you're prepping for the TEAS, knowing how to quickly eliminate wrong answers can save you valuable time and help reduce test anxiety. It’s all about the little strategies that empower you on exam day.

So, whether you’re doing practice tests, working through math problems at your study group, or just trying to get a better handle on these concepts, always keep a lookout for the interplay between even and odd integers. It can and will pop up in various questions, guiding you toward the correct answer.

Happy studying, and remember: Knowledge is your best ally in conquering the TEAS ATI Mathematics Test!