Finding the Missing Number: A Fun Approach to CCAT Questions

What is the missing number in a group of four numbers that have an average of 14, given the first three numbers are 11, 12, and 17?

• A. 11
• B. 15
• C. 16
• D. 18

Answer: (C)

To find the missing number in the group of four numbers with an average of 14, we start by recalling that the average of a set of numbers is calculated by dividing the sum of the numbers by the quantity of numbers in the set. First, since we know the average is 14 and there are four numbers, we can calculate the total sum of those four numbers. Specifically, we multiply the average by the total number of values: Total sum = Average × Number of values = 14 × 4 = 56. Next, we need to calculate the sum of the three known numbers: 11, 12, and 17. Total of known numbers = 11 + 12 + 17 = 40. Now, we can determine the missing number by subtracting the sum of the known numbers from the total sum: Missing number = Total sum - Sum of known numbers = 56 - 40 = 16. Thus, the missing number is 16. This aligns with the option that states 16 is the correct answer.

Let’s tackle a common challenge in the world of numbers: figuring out the missing value in a series of numbers based on their average. If you’re prepping for the Criteria Cognitive Aptitude Test (CCAT), mastering this concept could make all the difference.

You might wonder, how do you approach such a question? Let’s unravel this step by step to make it clear and relatable. Here’s a sample question that fits right into the CCAT landscape:

What is the missing number in a group of four numbers that have an average of 14, given the first three numbers are 11, 12, and 17?

To solve this, we need to stay calm and collected – no need to panic! The format may seem a little tricky at first, but breaking it down makes it more manageable.

First, let’s chat about the concept of an average. Think of it like a dinner table with four friends sharing a pizza. If each person wants their fair share, you need to divide the total pizza evenly. In numerical terms, to find an average, you add up all the numbers and divide by how many there are.

So, to kick off, we’ll need to find that total sum of our four mystery numbers. We know the average is 14, and we have four numbers in our dinner party. So, how do we get that total? You multiply:

Total sum = Average × Number of values = 14 × 4 = 56.

Easy, right? Now, let’s dig into our known numbers. We’ve got 11, 12, and 17 hanging out at the table. Add those together, and we’ve got:

Total of known numbers = 11 + 12 + 17 = 40.

Now, it’s crunch time! To find the missing number, we just have to subtract the sum of the known numbers (40) from the total sum (56):

Missing number = Total sum - Sum of known numbers = 56 - 40 = 16.

Voilà! The missing mystery number is 16! A quick look at our options confirms we’ve hit the jackpot—this aligns perfectly with option C, 16.

Understanding how to approach problems like these doesn’t just help you on the CCAT; it boosts your overall numerical reasoning skills. So, as you prepare, keep practicing with similar questions. And you know what? Sometimes, it’s about more than just the numbers. It’s about building your confidence and enjoying that “aha!” moment when everything clicks.

Plus, as you prepare, remember that math isn’t just a series of numbers—it’s a toolbox filled with problem-solving skills. Each question you tackle brings you a step closer to mastering that skill set. Who knew numbers could serve up so much insight about your cognitive abilities?

Now, who’s ready to tackle the next question? Let’s keep this momentum going and sharpen those minds for the CCAT. Happy studying!