Pattern – Reasoning Concepts for Competitive Exams
Pattern is a very broad reasoning topic, that needs you to identify the underlying sequence or logic. We will cover the most common types in this article
Number Transformation
In these questions, a number undergoes a transformation according to a specific rule. The rule may be applied separately to each digit or to the number as a whole. After the transformation, you may be asked to identify a digit, calculate a value using selected digits, or determine the position of a particular digit.
Common Types
- Adding or subtracting a fixed number from each digit
- Increasing odd digits and decreasing even digits
- Replacing digits according to a given condition
- Interchanging digits at specified positions
- Rearranging digits in ascending or descending order
- Performing different operations on different groups of digits
Example
Question: A number undergoes a transformation in which even digits are reduced by 2 and odd digits are increased by 2. What will be the transformed form of 256463127?
Transformation:
2 → 0, 5 → 7, 6 → 4, 4 → 2, 6 → 4, 3 → 5, 1 → 3, 2 → 0, 7 → 9
Result: 074245309
A subsequent question may ask for the product of the digit in the fifth position from the left and the second position from the right.
Letter Rearrangement
These questions provide a word or a group of letters and require the letters to be rearranged according to a specified rule. The most common rule is alphabetical order, but questions may also involve reverse alphabetical order or other arrangements.
Common Types
- Arranging letters in alphabetical order
- Arranging letters in reverse alphabetical order
- Finding letters that remain in the same position
- Finding the new position of a particular letter
- Counting letters whose positions change
- Identifying the letter at a specified position after rearrangement
Example
Question: If the letters in the word JUNIOR are arranged in alphabetical order, how many letters will remain in the same position?
Original: J U N I O R
Alphabetical order: I J N O R U
Comparing the two arrangements, only N remains in the third position.
Answer: One
Word Arrangement
In these questions, a group of words is arranged according to dictionary or alphabetical order. The question may ask for the word occupying a particular position after the arrangement.
Dictionary Order
Words are compared from left to right. The first letter at which two words differ determines their order. If the first letters are the same, compare the second letters, then the third, and so on.
Example
Arrange the following words in alphabetical order:
MNO, ABD, ATE, POT, KLO
The correct alphabetical arrangement is:
ABD → ATE → KLO → MNO → POT
If the question asks you to read the arrangement from right to left, the order becomes:
POT → MNO → KLO → ATE → ABD
Therefore, the third word when read from right to left is KLO.
Number Arrangement
These questions involve arranging the digits of a number according to a specified condition and then answering a question based on the resulting arrangement.
Common Types
- Arranging digits in ascending order
- Arranging digits in descending order
- Separating even and odd digits
- Moving specific digits to the beginning or end
- Interchanging digits at specified positions
- Finding the position of a digit after rearrangement
Example
Question: If the digits of 583214 are arranged in ascending order, which digit will be third from the left?
Original: 5 8 3 2 1 4
Ascending order: 1 2 3 4 5 8
The third digit from the left is 3.
Position-Based Pattern Questions
In these questions, the main task is to track the position of a letter, digit, or word before and after a transformation or rearrangement.
Common Types
- Position from the left
- Position from the right
- Position after rearrangement
- Number of elements between two elements
- Element occupying a particular position
- Comparing positions before and after transformation
Example
Consider the arrangement:
A 7 B 3 C 9 D 5 E
A question may ask:
What is the third element from the right?
Counting from the right gives:
E → 5 → D
Therefore, the third element from the right is D.
Alphanumeric Pattern
These questions combine letters and numbers in a single sequence. Some questions may also include symbols. You may be asked to identify elements based on their position, count elements satisfying a condition, or analyse the relationship between neighbouring elements.
Common Types
- Letter-number sequences
- Letter-number-symbol arrangements
- Counting numbers between letters
- Counting letters between numbers
- Finding elements at specific positions
- Finding elements that satisfy a positional condition
Example
Consider the sequence:
A 4 M 7 P 2 R 9 T
A question may ask how many letters are immediately preceded by an even number.
Here, M is preceded by 4, T is preceded by 9, and so on. The answer is obtained by checking the sequence according to the exact condition given.
Symbol-Based Patterns
Some pattern questions use numbers, letters, and symbols together. The symbols may be used as separators or may themselves be part of the condition being tested.
Example
Consider:
A # 4 B @ 7 C $ 2 D
A question may ask how many numbers are immediately followed by a letter, or how many symbols are between two numbers.
Interchange Questions
In interchange-based questions, two or more elements are swapped according to the instruction. The resulting arrangement is then used to answer a positional question.
Common Types
- Interchange two specified digits
- Interchange two letters
- Swap elements at specified positions
- Interchange groups of elements
- Perform multiple interchanges and identify the final position
Example
Consider the number 583216.
If the first and fifth digits are interchanged:
5 8 3 2 1 6 → 1 8 3 2 5 6
The resulting number is 183256.
Odd-Even Based Patterns
These questions use the properties of odd and even numbers or digits to create a transformation or arrangement.
Common Types
- Increasing odd digits and decreasing even digits
- Separating odd and even digits
- Arranging odd and even digits alternately
- Counting odd or even elements at specific positions
- Replacing elements based on whether they are odd or even
Example
If every odd digit is increased by 1 and every even digit is decreased by 1, then:
583214 → 674103
Here, each digit has been transformed individually according to whether it is odd or even.
Sequential Transformation
Some questions provide a sequence of transformations in which an operation is performed repeatedly. The result of one step becomes the input for the next step.
Example
Suppose a number is transformed by moving its largest digit to the left in each step.
Step 1: 583214
Step 2: 853214
The question may then ask which digit occupies a particular position after one or more steps.
Mixed Pattern Questions
Some questions combine more than one pattern. For example, a number may first be transformed and then its digits may be rearranged. Similarly, letters may first be arranged alphabetically and then a positional condition may be applied.
Example
A number may first undergo the following transformation:
Even digits → subtract 1
Odd digits → add 1
The resulting digits may then be arranged in ascending order. The question can subsequently ask for the digit at a particular position.
Important Pattern Types to Remember
- Number Transformation: Apply a mathematical rule to digits.
- Letter Rearrangement: Rearrange letters according to alphabetical or another specified order.
- Word Arrangement: Arrange words according to dictionary order.
- Number Arrangement: Rearrange digits according to ascending, descending, or specified conditions.
- Position-Based Questions: Identify or compare elements at particular positions.
- Alphanumeric Pattern: Analyse sequences containing letters and numbers.
- Symbol Pattern: Analyse sequences containing letters, numbers, and symbols.
- Interchange: Swap specified elements and analyse the resulting arrangement.
- Odd-Even Pattern: Apply different rules based on whether elements are odd or even.
- Sequential Transformation: Apply a rule repeatedly through multiple steps.
- Mixed Pattern: Combine two or more transformations or arrangements.