Number Series Questions - CCAT Test Prep

This type of question tests your ability to recognize patterns in a sequence of numbers. The goal is to determine the next number in the series by identifying the relationship between the numbers. Each number in the series may relate to the others through addition, subtraction, multiplication, or some other mathematical operation. By breaking down the series step-by-step, you can often uncover the underlying pattern.

number-series

How to Identify the Next Number in a Series

Question 1 - Difference

What would be the next number in the following series?
1, 4, 10, 22, 46, 94, ?

  • A) 182
  • B) 188
  • C) 190
  • D) 194
  • E) 198

Step-by-Step Solution:

First, examine the differences between each consecutive pair of numbers:


Difference between 4 and 1 = 4 - 1 = 3
Difference between 10 and 4 = 10 - 4 = 6
Difference between 22 and 10 = 22 - 10 = 12
Difference between 46 and 22 = 46 - 22 = 24
Difference between 94 and 46 = 94 - 46 = 48

Next, list the differences:


Differences: 3, 6, 12, 24, 48

Now, look at the differences of the differences:


Difference between 6 and 3 = 6 - 3 = 3
Difference between 12 and 6 = 12 - 6 = 6
Difference between 24 and 12 = 24 - 12 = 12
Difference between 48 and 24 = 48 - 24 = 24

This gives you a new set of differences:


Differences of differences: 3, 6, 12, 24

Now, observe the pattern in the differences of differences. Each is double the previous:

  • 3, 6 (3 × 2), 12 (6 × 2), 24 (12 × 2)

Continuing this pattern, the next difference should be:


Next difference = 24 × 2 = 48

To find the next difference in the original series:


Next difference = 48 + 48 = 96

Now add this new difference to the last number in the series:


Next number = 94 + 96 = 190

Answer: $190

Question 2 - Multiplication Difference

What would be the next number in the following series?
2, 6, 18, 54, ?

  • A) 162
  • B) 168
  • C) 172
  • D) 176
  • E) 180

Step-by-Step Solution:

To find the next number in the series, observe the pattern of multiplication:


2 × 3 = 6
6 × 3 = 18
18 × 3 = 54

Notice that each number is being multiplied by 3 to get the next number in the series. Following this pattern:


Next number = 54 × 3 = 162

Answer: 162

Question 3 - Division

What would be the next number in the following series?
100, 50, 25, 12.5, ?

  • A) 6.25
  • B) 7.5
  • C) 8.5
  • D) 9.5
  • E) 10

Step-by-Step Solution:

In this series, each number is being divided by 2 to find the next number:


100 ÷ 2 = 50
50 ÷ 2 = 25
25 ÷ 2 = 12.5

Following this pattern:


Next number = 12.5 ÷ 2 = 6.25

Answer: 6.25

Question 4 - Previous Number

What would be the next number in the following series?
1, 3, 7, 13, 21, ?

  • A) 30
  • B) 31
  • C) 32
  • D) 33
  • E) 34

Step-by-Step Solution:

To find the next number, observe the pattern in the series:


3 - 1 = 2
7 - 3 = 4
13 - 7 = 6
21 - 13 = 8

The differences are increasing by 2 each time:


Next difference = 8 + 2 = 10

Now, add this difference to the last number:


Next number = 21 + 10 = 31

Answer: 31

Question 5 - Pattern by Next Number

What would be the next number in the following series?
2, 5, 10, 17, 26, ?

  • A) 37
  • B) 38
  • C) 39
  • D) 40
  • E) 41

Step-by-Step Solution:

In this series, each number follows a specific pattern based on adding consecutive odd numbers:


2 + 3 = 5
5 + 5 = 10
10 + 7 = 17
17 + 9 = 26

The numbers being added are increasing by 2 each time. The next odd number to add is 11:


Next number = 26 + 11 = 37

Answer: 37

Question 6- Pattern by multiplication

What would be the next number in the following series?
3, 6, 12, 24, 48, ?

  • A) 84
  • B) 96
  • C) 102
  • D) 120
  • E) 144

Step-by-Step Solution:

In this series, each number is doubled to get the next number:


3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
24 × 2 = 48

Continuing this pattern:


Next number = 48 × 2 = 96

Answer: 96

Question 7 - Pattern by Pow

What would be the next number in the following series?
1, 4, 9, 16, 25, ?

  • A) 30
  • B) 31
  • C) 32
  • D) 33
  • E) 36

Step-by-Step Solution:

This series consists of perfect squares:


1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25

The next perfect square is:


6^2 = 36

Answer: 36

Other Famous Patterns

Certainly! Here’s the list of different patterns used in number series and the methods to calculate the next number, formatted outside of a code block:

  1. Addition Pattern: Numbers are obtained by adding a constant or increasing amounts.
    Example: 2, 4, 6, 8 (Add 2 each time).
  2. Subtraction Pattern: Numbers are obtained by subtracting a constant or decreasing amounts.
    Example: 10, 7, 4, 1 (Subtract 3 each time).
  3. Multiplication Pattern: Each number is multiplied by a constant.
    Example: 3, 6, 12, 24 (Multiply by 2 each time).
  4. Division Pattern: Each number is divided by a constant.
    Example: 100, 50, 25, 12.5 (Divide by 2 each time).
  5. Exponential Growth: Each number is obtained by raising a base to a power.
    Example: 2^1, 2^2, 2^3, 2^4 (2, 4, 8, 16).
  6. Square Pattern: Numbers are perfect squares.
    Example: 1, 4, 9, 16 (1^2, 2^2, 3^2, 4^2).
  7. Cube Pattern: Numbers are perfect cubes.
    Example: 1, 8, 27, 64 (1^3, 2^3, 3^3, 4^3).
  8. Fibonacci Sequence: Each number is the sum of the two preceding ones.
    Example: 0, 1, 1, 2, 3, 5, 8 (0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3).
  9. Alternating Patterns: The series follows two or more different patterns.
    Example: 1, 2, 4, 3, 6, 5 (Doubling and adding).
  10. Factorial Pattern: Each number is the factorial of a natural number.
    Example: 1!, 2!, 3!, 4! (1, 2, 6, 24).
  11. Triangular Numbers: Each number is the sum of the first n natural numbers.
    Example: 1, 3, 6, 10 (1, 1+2, 1+2+3, 1+2+3+4).
  12. Geometric Series: Each number is obtained by multiplying the previous number by a constant ratio.
    Example: 2, 6, 18, 54 (Multiply by 3 each time).
  13. Prime Number Pattern: Numbers are prime numbers in order.
    Example: 2, 3, 5, 7, 11, 13.
  14. Factor Patterns: Involves finding factors of a number to establish the series.
    Example: 1, 2, 3, 6 (Factors of 6).
  15. Power Pattern: Each term is a power of a base.
    Example: 3^0, 3^1, 3^2, 3^3 (1, 3, 9, 27).

Strategy

  1. Examine the series and look for patterns in the numbers, such as simple arithmetic operations.
  2. Calculate the differences between consecutive numbers to see if a pattern emerges.
  3. If needed, calculate the differences of the differences to identify more complex relationships.
  4. Use any patterns discovered to predict the next number in the series.

By following these steps, you can systematically analyze numerical sequences and determine the next number based on established patterns.

20 Practice Questions

What would be the next number in the following series?
2, 6, 12, 20, 30, ?

  • A) 38
  • B) 42
  • C) 48
  • D) 50
  • E) 54

What would be the next number in the following series?
5, 11, 19, 29, ?

  • A) 39
  • B) 41
  • C) 43
  • D) 45
  • E) 47

What would be the next number in the following series?
3, 9, 27, 81, ?

  • A) 162
  • B) 164
  • C) 165
  • D) 168
  • E) 170

What would be the next number in the following series?
1, 2, 4, 8, 16, ?

  • A) 30
  • B) 32
  • C) 34
  • D) 36
  • E) 40

What would be the next number in the following series?
100, 90, 80, 70, ?

  • A) 60
  • B) 50
  • C) 55
  • D) 65
  • E) 70

What would be the next number in the following series?
1, 1, 2, 3, 5, ?

  • A) 6
  • B) 7
  • C) 8
  • D) 9
  • E) 10

What would be the next number in the following series?
7, 14, 28, 56, ?

  • A) 84
  • B) 112
  • C) 126
  • D) 140
  • E) 154

What would be the next number in the following series?
10, 20, 40, 80, ?

  • A) 150
  • B) 160
  • C) 170
  • D) 180
  • E) 190

What would be the next number in the following series?
6, 11, 17, 24, ?

  • A) 30
  • B) 31
  • C) 32
  • D) 33
  • E) 34

What would be the next number in the following series?
1, 2, 4, 7, ?

  • A) 9
  • B) 10
  • C) 11
  • D) 12
  • E) 13

What would be the next number in the following series?
0, 1, 1, 2, 3, 5, ?

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

What would be the next number in the following series?
1, 4, 9, 16, ?

  • A) 20
  • B) 25
  • C) 30
  • D) 35
  • E) 40

What would be the next number in the following series?
4, 8, 12, 16, ?

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

What would be the next number in the following series?
15, 25, 35, 45, ?

  • A) 55
  • B) 60
  • C) 65
  • D) 70
  • E) 75

What would be the next number in the following series?
2, 3, 5, 7, ?

  • A) 9
  • B) 10
  • C) 11
  • D) 12
  • E) 13

What would be the next number in the following series?
9, 18, 36, 72, ?

  • A) 108
  • B) 120
  • C) 144
  • D) 162
  • E) 180

What would be the next number in the following series?
2, 5, 10, 17, ?

  • A) 24
  • B) 25
  • C) 26
  • D) 27
  • E) 28

What would be the next number in the following series?
20, 30, 50, 80, ?

  • A) 100
  • B) 110
  • C) 120
  • D) 130
  • E) 140

What would be the next number in the following series?
5, 12, 21, 32, ?

  • A) 40
  • B) 41
  • C) 42
  • D) 43
  • E) 44

What would be the next number in the following series?
1, 3, 6, 10, ?

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

Answers

  1. A) 38
  2. A) 39
  3. A) 162
  4. B) 32
  5. A) 60
  6. C) 8
  7. A) 84
  8. B) 160
  9. A) 30
  10. B) 10
  11. A) 8
  12. B) 25
  13. A) 20
  14. A) 55
  15. C) 11
  16. A) 108
  17. A) 24
  18. A) 100
  19. A) 40
  20. C) 15
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