SSC MTS Circular Seating Arrangement — Study Material, 5 PYQs & Practice MCQs | ZestExam
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SSC MTS Circular Seating Arrangement
Study Material — 5 PYQs (2024–2024) · Concept Notes · Shortcuts
SSC MTS Circular Seating Arrangement is a frequently tested subtopic — 5 previous year questions from 2024–2024 papers are included below with concept notes, key rules and shortcut tricks.
SSC MTS Circular Seating Arrangement — Past Exam Questions
5 questions from actual SSC MTS papers · all shown free · click option to reveal solution
Exam Q 12024Previous Year Pattern
Four students—Priya, Qasim, Rohan, and Sana—sit around a circular table. Rohan sits immediately to the right of Priya. Sana sits immediately to the right of Rohan. Where is Qasim sitting?
Test Circular Seating Arrangement under exam conditions
Three people—Aman, Bina, and Chetan—sit around a circular table. Aman sits immediately to the left of Bina. Which statement is definitely true?
Exam Q 32024Previous Year Pattern
Four colleagues—Vikram, Xena, Yash, and Zara—sit around a circular conference table. Vikram sits directly opposite Yash. Xena sits immediately to the right of Vikram. Which of the following must be true?
Exam Q 42024Previous Year Pattern
Four friends—Arun, Bhavna, Chitra, and Deepak—sit around a circular table. Arun sits immediately to the right of Bhavna. Chitra sits immediately to the left of Bhavna. Where does Deepak sit?
Exam Q 52024Previous Year Pattern
Six people sit around a circular table: A, B, C, D, E, and F. A sits immediately to the right of B. C sits immediately to the right of A. D sits immediately to the right of C. If E sits immediately to the left of B, who sits immediately to the right of E?
Concept Notes
Circular Seating Arrangement— Rules & Concept
💡
Core Concept
Read this first — the foundation of the topic
→Core Concept
In circular seating, positions are relative to each other. There is no first or last position. The key is to fix one person's position first, then arrange others relative to that person
💡Key Rules
1) Always fix one person's position to eliminate rotational possibilities 2) Clockwise and anti-clockwise directions matter 3) 'Opposite' means diametrically across 4) Adjacent means immediate left or right 5) Use process of elimination systematically.
🔢
Formula Block
Memorise — at least one formula appears in every paper
Total circular arrangements of n people = (n-1)! This is because we fix one position to avoid counting rotations as different arrangements. For restrictions like couples sitting together, treat them as single units.
📊
Exam Patterns
What examiners ask — read before attempting PYQs
→Common question types include
immediate neighbors, opposite positions, counting positions between people, and conditional arrangements. Most questions give 6-8 people with 4-6 conditions
⚡Shortcut Trick 1 - The Fixed Position Method
Always start by placing one person at the 'top' of the circle. This eliminates confusion about rotational arrangements. Mark positions as 1,2,3... clockwise from this fixed person
⚡Shortcut Trick 2 - The Opposite Formula
In a circle of n people, if person A is at position x, then the person opposite to A is at position x + n/2 (if n is even). For odd numbers, no one sits exactly opposite
✏️Worked Example 1
Six friends A,B,C,D,E,F sit around a circular table. B sits two places to the right of A. C sits opposite to A. D sits immediately left of C.
Where does E sit
→Solution Step-by-Step
1
Fix A at position 1 (top)
2
B sits two places right of A, so B at position 3
3
C sits opposite A. In 6-person circle, opposite of position 1 is position 4. So C at position 4
4
D sits immediately left of C. Left of position 4 is position 3. But B is already there. This means left of C is position 5. Wait - let me recalculate. If we number 1,2,3,4,5,6 clockwise, then left of 4 is position 3. Since B occupies 3, there's a contradiction
🔑Let me recheck
immediate left of position 4 is position 5 (going anti-clockwise). So D at position 5.
Step 5: Remaining positions are 2 and 6. E and F occupy these
→Answer
E sits at either position 2 or 6
✏️Worked Example 2
Seven people sit in a circle. P sits third to the right of Q. R sits second to the left of P. How many people sit between Q and R when counted clockwise from Q
→Solution Step-by-Step
1
Fix Q at position 1
2
P sits third to right of Q, so P at position 4
3
R sits second to left of P
→Left of position 4 going anti-clockwise
position 3 is first left, position 2 is second left. So R at position 2
Step 4: Count from Q(position 1) to R(position 2) clockwise: only position 7 comes between them
Answer: 1 person sits between Q and R
⚡Shortcut Trick 3 - The Gap Counting Formula
To count people between positions A and B clockwise: if B > A, count = B - A - 1. If B < A, count = n - A + B - 1 (where n is total people)
→Most Common Trap
Students often confuse 'left' and 'right' directions
💡Remember
in clockwise numbering, right means higher numbers, left means lower numbers. Also, 'second to the right' means there's one person in between, not sitting in the second chair. Many students miss this and count wrong positions.
Key Points to Remember
Always fix one person's position first to avoid rotational confusion
In circular arrangement of n people, total arrangements = (n-1)!
Opposite position formula: if person at position x, opposite at x + n/2 (for even n)
Second to the right means one person sits in between, not the second position
Clockwise numbering: right = higher numbers, left = lower numbers
Gap counting formula: between A and B clockwise = B-A-1 (if B>A)
For odd number of people, no one sits exactly opposite to anyone
Adjacent means immediate left or immediate right neighbor only
Use elimination method when multiple conditions are given
Draw the circle and number positions 1,2,3... for visual clarity
Exam-Specific Tips
Circular arrangements of n distinct objects = (n-1)! permutations
In 6-person circle, opposite positions are (1,4), (2,5), (3,6)
In 8-person circle, positions 1 and 5 are diametrically opposite
SSC CGL typically gives 6-8 people in circular seating questions
Maximum people between any two positions in n-person circle = n-3
In odd-numbered circles (5,7,9 people), no exact opposite positions exist
Most SSC circular arrangement sets contain 3-5 questions with 4-6 conditions
Immediate left of position 1 in n-person circle is position n
60-Second Revision — Circular Seating Arrangement
Remember: Fix one person first, then arrange others relative to that position
Formula: Opposite position = current position + n/2 (for even n only)
Trap: 'Second to right' means one person between, not second position
Trick: Number positions 1,2,3... clockwise for systematic solving
Direction: Right = clockwise = higher numbers, Left = anti-clockwise = lower numbers
Gap formula: People between A and B = |B-A|-1 positions
Quick check: Total positioned people should equal given number