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Order and Ranking
Page 2


Order and Ranking
Understanding Order and Ranking
Core Concept
Determine positions of persons or objects 
in a line or queue, often from both ends 
(left/right or top/bottom).
What You'll Find
Questions about total persons, positions 
after changes, or numbers between 
positions.
Page 3


Order and Ranking
Understanding Order and Ranking
Core Concept
Determine positions of persons or objects 
in a line or queue, often from both ends 
(left/right or top/bottom).
What You'll Find
Questions about total persons, positions 
after changes, or numbers between 
positions.
Types of Ranking Problems
1
Single Position Problems
Total persons and position of one 
person are given.
2
Multiple Position Problems
Position of more than one person is 
given.
3
Overlapping Conditions
When (left + right) positions > Total 
number of students.
4
Non-Overlapping Conditions
When Total number of students > (left + 
right) positions.
Page 4


Order and Ranking
Understanding Order and Ranking
Core Concept
Determine positions of persons or objects 
in a line or queue, often from both ends 
(left/right or top/bottom).
What You'll Find
Questions about total persons, positions 
after changes, or numbers between 
positions.
Types of Ranking Problems
1
Single Position Problems
Total persons and position of one 
person are given.
2
Multiple Position Problems
Position of more than one person is 
given.
3
Overlapping Conditions
When (left + right) positions > Total 
number of students.
4
Non-Overlapping Conditions
When Total number of students > (left + 
right) positions.
What We Need to Find
Position from 
other side
Converting left 
rank to right or 
vice versa.
Total number of 
persons
Finding the 
complete count in 
the arrangement.
Persons in 
between
Counting 
individuals 
between two 
positions.
Minimum/maxi
mum count
Finding possible 
extremes in 
arrangements.
Page 5


Order and Ranking
Understanding Order and Ranking
Core Concept
Determine positions of persons or objects 
in a line or queue, often from both ends 
(left/right or top/bottom).
What You'll Find
Questions about total persons, positions 
after changes, or numbers between 
positions.
Types of Ranking Problems
1
Single Position Problems
Total persons and position of one 
person are given.
2
Multiple Position Problems
Position of more than one person is 
given.
3
Overlapping Conditions
When (left + right) positions > Total 
number of students.
4
Non-Overlapping Conditions
When Total number of students > (left + 
right) positions.
What We Need to Find
Position from 
other side
Converting left 
rank to right or 
vice versa.
Total number of 
persons
Finding the 
complete count in 
the arrangement.
Persons in 
between
Counting 
individuals 
between two 
positions.
Minimum/maxi
mum count
Finding possible 
extremes in 
arrangements.
Essential Formulas - Part 1
Converting ranks
Total 3 (given rank 3 1) = required rank
Finding total
When ranks of common person from both sides: (R ¡ 
+ R ¢) 3 1
Total with middle persons
(R ¡ + R ¢) + number of middle persons
Overlapping case
(R ¡ + R ¢) - (number of middle persons + 2)
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