Numerical Reasoning Questions and Answers - Number Series

Numerical reasoning tests are like exciting puzzles that challenge your ability to understand and analyse number patterns. To excel in numerical reasoning, you need to be able to identify the hidden pattern among numbers and apply that pattern consistently in order to find missing numbers or complete number sets. 

In this blog post, we'll go through the steps to uncover number patterns and provide five examples with detailed analysis to help you answer selective schools numerical reasoning tests with confidence.

Number Patterns in Numerical ReasoningTest

Determine the direction: Observe whether the numbers in the series are increasing, decreasing or alternating.

1. Increasing series

Addition and multiplication: If the numbers are going up, addition or multiplication is likely involved.

2. Decreasing series

Subtraction and division: subtraction or division is likely involved if the numbers are going down.

3. Alternating series

Combination of operations: In cases where the series alternates between increasing and decreasing numbers, a combination of addition/multiplication and subtraction/division may be at play.

Applying Number Patterns

Once you've identified the pattern, apply it consistently to find missing numbers or complete grouped number sets.

Take a look at the examples and analysis below:

Example 1: [2, 4, 8, ?]

The numbers in the series seem to be doubling.

Applying the pattern: By doubling each number, the missing number would be 16.

Example 2: [25, 20, 15, ?]

The numbers in the series are decreasing by 5.

Applying the pattern: By subtracting 5 from each number, the missing number would be 10.

Example 3: [9, 16, 23, ?]

The numbers in the series are increasing by 7.

Applying the pattern: By adding 7 to each number, the missing number would be 30.

Example 4: [18, 12, 8, ?]

Analyzing the pattern: The numbers in the series are decreasing by dividing by 2 and then subtracting 2.

Applying the pattern: By dividing each number by 2 and subtracting 2, the missing number would be 4.

Example 5: [3, 10, 19, ?]

The numbers in the series are increasing by adding consecutive odd numbers (1, 3, 5...).

Applying the pattern: By adding the next odd number (7) to the last number (19), the missing number would be 26.

Number Patterns - Matrices

Number pattern questions come in various forms, including matrices. Solving matrix questions requires a combination of logical thinking, visualization and pattern recognition.

Approach to Solving Matrix Number Pattern Questions

The approach to solving matrix number pattern questions involves three main steps:

Step 1: Identify the Features of the Matrix

This step involves identifying the type of numbers in the matrix, whether they are letters or a combination of letters and numbers, and whether the numbers are increasing or decreasing. Additional features that may be identified include dead numbers, where certain numbers in the matrix do not form part of the pattern.

Step 2: Identify the Visual Pattern

This step entails looking for patterns in the arrangement of the numbers in the matrix. The visual patterns may include horizontal, vertical, diagonal, L-shaped, zigzag or other odd patterns.

Step 3: Identify the Mathematical Properties of the Numbers

After identifying the pattern, the next step involves examining the mathematical properties of the numbers in the matrix. The mathematical properties may involve addition, subtraction, multiplication or division.

Examples

Let us explore the following examples of matrix number pattern questions.

| 9 | 12 | 15 | 

| 16 | 20 | 24 | 

| 25 | 30 | ? |

To find the missing number, let's observe the pattern in the sequence:

In the first row, each number increases by 3 from left to right: 9 + 3 = 12, 12 + 3 = 15.

In the second row, each number increases by 4 from left to right: 16 + 4 = 20, 20 + 4 = 24.

Based on this pattern, it can be inferred that in the third row, each number should increase by 5 from left to right.

Therefore, to find the missing number, we add 5 to the last number (30) in the third row:

30 + 5 = 35.

Thus, the missing number in the sequence is 35.

Here's another example:

| 12 | 9 | 6 | 

| 11 | 8 | 5 | 

| 10 | 7 | ? |

To solve this sequence, let's apply the same logical step-by-step process as before:

The numbers are decreasing from left to right.

There is a horizontal direction.

The numbers in the first column can be obtained by subtracting 1 from the previous number.

The numbers in the first row are decreasing by 3, and the numbers in the second row are decreasing by 3 as well.

The numbers in the third row are decreasing by 3.

Based on this pattern, we can determine that the missing number is 4.

Tips for Successful Numerical Reasoning Test Preparation

To excel in numerical reasoning tests, keep these tips in mind:

Start with the Basics: Understand number patterns and basic arithmetic operations. Practice solving simple problems to build a strong foundation.

Time Management: Set a timer while practicing to improve your speed and accuracy. This will help you become more comfortable under test conditions.

Familiarize Yourself with the Test Format: Get to know the specific question types in the numerical reasoning test you're preparing for. Work on sample questions to become familiar with the format.

Seek Guidance: Don't hesitate to ask for help from a teacher, tutor, or study group if you're struggling. They can provide explanations and offer additional practice materials.

Final Words

Numerical reasoning tests can be intimidating, but with practice and a systematic approach, you can master them. To uncover number patterns, start by determining the series' direction and testing possible operations. 

Once you've identified the pattern, apply it consistently to find missing numbers or complete grouped number sets. Keep these guidelines in mind and practice regularly and you'll ace your entrance exam.