Quick Average - CCAT Test Prep

This type of question tests your understanding of finding an unknown value when given an average (arithmetic mean). Calculating an average and working backward to find missing values can be useful in many real-world situations, such as budgeting, grading, or estimating expenses. Let’s break it down into simple steps to solve the problem.

How to Find an Unknown Value Given the Average

Question 1 - Calculating an Unknown Number Using Average

A group of four numbers has an average (arithmetic mean) of 17. The first three numbers are 9, 32, and 19. What is the other number?

A) 8
B) 12
C) 13
D) 15
E) 17

Step 1: Understand the Problem

The average of four numbers is 17. The average is calculated by adding all four numbers and dividing by 4.

Step 2: Set Up the Equation

We know three of the four numbers: 9, 32, and 19. Let’s represent the unknown number as X.

To find X, we start by calculating the total sum of the four numbers. Since the average is 17:

Total sum 
    = 17 × 4 
    = 68

Step 3: Calculate the Total of Known Numbers

Add the three given numbers:

Sum of known numbers 
    = 9 + 32 + 19 
    = 60

Step 4: Find the Missing Number

The unknown number can be found by subtracting the sum of the known numbers from the total sum:

X 
    = 68 - 60 
    = 8

Answer: 8

By breaking down the average calculation into smaller steps, you can easily determine the missing value without much complexity.

Question 2 - Finding the Missing Value

The average of five numbers is 24. The first four numbers are 28, 22, 19, and 25. What is the fifth number?

A) 26
B) 24
C) 28
D) 20
E) 22

Step 1: Set Up the Total

Total sum 
    = 24 × 5 
    = 120

Step 2: Calculate the Sum of Known Numbers

Sum of known numbers 
    = 28 + 22 + 19 + 25 
    = 94

Step 3: Find the Missing Number

Fifth number 
    = 120 - 94 
    = 26

Answer: 26

Question 3 - Average Calculation

A group of six numbers has an average of 12. Five of the numbers are 8, 15, 10, 13, and 11. What is the sixth number?

A) 14
B) 17
C) 20
D) 12
E) 18

Step 1: Set Up the Total

Total sum 
    = 12 × 6 
    = 72

Step 2: Calculate the Sum of Known Numbers

Sum of known numbers 
    = 8 + 15 + 10 + 13 + 11 
    = 57

Step 3: Find the Missing Number

Sixth number 
    = 72 - 57 
    = 15

Answer: 15

How to Solve These Questions Easily

Step 1: Calculate the Total Sum

Multiply the average by the number of items to find the total sum.

Step 2: Add the Known Values

Calculate the sum of the known values.

Step 3: Subtract to Find the Missing Value

Subtract the sum of the known values from the total to find the missing value.

Using this method, you can easily determine the missing number without making the calculations overly complicated.

20 Practice Questions - Average Calculation

The average of four numbers is 25. The first three numbers are 20, 30, and 15. What is the fourth number?

A) 25
B) 30
C) 35
D) 40
E) 45

A group of five numbers has an average of 18. The first four numbers are 14, 19, 16, and 20. What is the fifth number?

A) 19
B) 21
C) 22
D) 23
E) 24

The average of five numbers is 22. The first four numbers are 20, 25, 18, and 24. What is the fifth number?

A) 21
B) 23
C) 26
D) 27
E) 28

The average of six numbers is 15. The first five numbers are 12, 18, 14, 13, and 15. What is the sixth number?

A) 14
B) 15
C) 16
D) 17
E) 18

A group of four numbers has an average of 28. The first three numbers are 30, 25, and 27. What is the fourth number?

A) 28
B) 30
C) 32
D) 34
E) 36

The average of four numbers is 10. The first three numbers are 8, 12, and 11. What is the fourth number?

A) 9
B) 7
C) 10
D) 11
E) 13

A group of five numbers has an average of 20. The first four numbers are 15, 22, 18, and 25. What is the fifth number?

A) 19
B) 20
C) 22
D) 23
E) 25

The average of three numbers is 12. The first two numbers are 10 and 15. What is the third number?

A) 11
B) 9
C) 12
D) 10
E) 8

The average of four numbers is 14. The first three numbers are 13, 16, and 12. What is the fourth number?

A) 15
B) 14
C) 13
D) 16
E) 17

A group of four numbers has an average of 18. The first three numbers are 19, 16, and 17. What is the fourth number?

A) 20
B) 18
C) 19
D) 17
E) 21

The average of six numbers is 19. The first five numbers are 18, 20, 21, 19, and 16. What is the sixth number?

A) 20
B) 21
C) 17
D) 18
E) 22

A group of five numbers has an average of 25. The first four numbers are 26, 24, 25, and 23. What is the fifth number?

A) 25
B) 26
C) 24
D) 22
E) 28

The average of three numbers is 20. The first two numbers are 18 and 22. What is the third number?

A) 20
B) 22
C) 18
D) 19
E) 21

The average of four numbers is 24. The first three numbers are 25, 23, and 20. What is the fourth number?

A) 25
B) 24
C) 23
D) 22
E) 21

A group of six numbers has an average of 16. The first five numbers are 15, 18, 14, 17, and 16. What is the sixth number?

A) 16
B) 15
C) 17
D) 18
E) 19

The average of five numbers is 26. The first four numbers are 28, 25, 24, and 27. What is the fifth number?

A) 26
B) 28
C) 25
D) 24
E) 29

A group of five numbers has an average of 14. The first four numbers are 12, 15, 16, and 13. What is the fifth number?

A) 14
B) 15
C) 13
D) 12
E) 16

The average of four numbers is 30. The first three numbers are 32, 28, and 31. What is the fourth number?

A) 29
B) 30
C) 28
D) 27
E) 26

The average of three numbers is 18. The first two numbers are 20 and 16. What is the third number?

A) 18
B) 16
C) 20
D) 19
E) 17

A group of four numbers has an average of 22. The first three numbers are 23, 21, and 24. What is the fourth number?

A) 20
B) 21
C) 22
D) 19
E) 23

Answers

C) 35
C) 22
D) 27
E) 18
A) 28
B) 7
B) 20
C) 12
B) 14
A) 20
C) 17
C) 24
A) 20
B) 24
B) 15
A) 26
A) 14
B) 30
A) 18
D) 19

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