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Linear Arrangement (Two Rows)

Introduction

Two-row linear arrangements involve people seated in two parallel rows facing each other or in opposite directions. These puzzles test spatial reasoning, direction sense, and relative positioning skills.

This pattern is a common higher-level reasoning type, especially in banking and government exams, where one must handle opposite-facing clues precisely.

Pattern: Linear Arrangement (Two Rows)

Pattern

Key Concept: Fix one row first, then use “facing direction” to interpret left/right correctly for the opposite row. When two rows face each other:

  • Row 1 (facing South) → Left/Right are reversed compared to the observer’s view.
  • Row 2 (facing North) → Left/Right are the same as the observer’s view.

Step-by-Step Example

Question

Eight people are seated in two parallel rows of four each facing each other.
Row 1 (facing South): A, B, C, D
Row 2 (facing North): P, Q, R, S

Clues:
1️⃣ A sits immediately left of B.
2️⃣ C sits second to the right of B.
3️⃣ P sits opposite B.
4️⃣ S sits at the extreme right end of Row 2.

Who is sitting opposite C?

Options:

  • A) P
  • B) Q
  • C) R
  • D) S

Solution

  1. Step 1: Fix Row 1 first

    A is immediately left of B → [A B]. C is second to the right of B → pattern fits as [A B C D].

  2. Step 2: Apply opposite clue

    P sits opposite B → place P directly facing B in Row 2.

  3. Step 3: Apply Row 2 clue

    S sits at the extreme right end → S is at Row 2’s far-right seat.

  4. Step 4: Fill remaining Row 2 positions

    Remaining people Q and R fill positions 1 and 3. Opposite of C (Row 1’s 3rd position) is Row 2’s 3rd seat → R.

  5. Final Answer:

    R → Option C

  6. Quick Check:

    Top row (A B C D) and bottom row (Q P R S) satisfy all clues. ✅

Quick Variations

  • 1. Both rows facing the same direction (tricky - opposites flip).
  • 2. Unequal number of people per row (fill with blanks first).
  • 3. Cross-reference clues like “X sits to the left of Y’s opposite.”

Trick to Always Use

  • Step 1 → Draw two parallel lines and mark columns 1-n for both rows.
  • Step 2 → Fill one row completely using adjacency/distance clues first.
  • Step 3 → Add the opposite-facing row by column mapping.
  • Step 4 → Check every “left/right” relative to facing direction before finalizing.

Summary

Summary

  • Anchor one row using distance and adjacency clues first.
  • Interpret left/right relative to each person’s facing direction.
  • Map opposites vertically column-by-column for clarity.
  • Cross-verify all positional and facing-direction clues before concluding.

Example to remember:
If Row 1 = A B C D and Row 2 = Q P R S, then B ↔ P, C ↔ R.

Practice

(1/5)
1. Eight people are seated in two parallel rows of four each facing each other. Top row (Row-1, left→right): A, B, C, D. Bottom row (Row-2, left→right) are four of P, Q, R, S. It is known that P sits opposite A, Q sits immediately right of P (bottom-row view), and S sits at the extreme right of Row-2. Who sits opposite C?
easy
A. R
B. P
C. Q
D. S

Solution

  1. Step 1: Fix Row-1

    Top row columns 1-4: A, B, C, D.

  2. Step 2: Place P opposite A

    P opposite A → P in bottom col1.

  3. Step 3: Place Q and S

    Q immediate right of P (bottom view) → Q in bottom col2. S at extreme right → S in bottom col4.

  4. Step 4: Fill remaining bottom seat

    Remaining person R goes to bottom col3 → bottom row = P, Q, R, S (cols1-4).

  5. Final Answer:

    R → Option A

  6. Quick Check:

    Opposites: A↔P (col1), B↔Q (col2), C↔R (col3), D↔S (col4) ✅
Hint: Place fixed opposite pairs first, then apply same-row adjacency and end clues.
Common Mistakes: Interpreting 'right' relative to observer instead of the person's facing direction.
2. Ten people sit in two rows of five each facing each other. Top row (Row-1, left→right): A, B, C, D, E. Bottom row (Row-2, left→right) include P, Q, R, S, T. If P sits opposite C, Q sits immediate right of P (bottom view), S sits opposite A, and T sits at extreme right of Row-2, who is opposite D?
easy
A. T
B. R
C. Q
D. P

Solution

  1. Step 1: Fix Row-1 columns

    Top row columns 1-5: A, B, C, D, E.

  2. Step 2: Place P opposite C and S opposite A

    P opposite C → P in bottom col3. S opposite A → S in bottom col1.

  3. Step 3: Place Q relative to P and T at end

    Q immediate right of P (bottom view) → Q in bottom col4. T at extreme right → T in bottom col5.

  4. Step 4: Fill remaining slot

    Remaining bottom person R goes to bottom col2 → bottom row = S, R, P, Q, T → opposite of D (col4) = Q.

  5. Final Answer:

    Q → Option C

  6. Quick Check:

    P opposite C (col3) ✅ Q right of P (col4) ✅ S opposite A (col1) ✅ T extreme right (col5) ✅ → Opposite D = Q ✅
Hint: Place opposites and end seats first, then fill adjacency slots and leftovers.
Common Mistakes: Placing adjacency in bottom row without first fixing opposite constraints.
3. Eight people sit in two rows (4 each) facing each other. Top row (left→right): G, H, I, J. Bottom row (left→right) are K, L, M, N. Clues: K sits opposite H; L sits immediate left of K (bottom view); N sits opposite J; M is not at any end. Who sits opposite I?
easy
A. K
B. L
C. N
D. M

Solution

  1. Step 1: Fix top row

    Top row cols1-4 = G, H, I, J.

  2. Step 2: Place K opposite H

    K opposite H → K in bottom col2.

  3. Step 3: Place L left of K and N opposite J

    L immediate left of K (bottom view) → L in bottom col1. N opposite J → N in bottom col4.

  4. Step 4: Place M (not at any end)

    Remaining bottom slot is col3 → M in col3. Bottom row = L, K, M, N.

  5. Step 5: Opposite of I

    I is top col3 → opposite = M.

  6. Final Answer:

    M → Option D

  7. Quick Check:

    Bottom row L (col1), K (col2), M (col3), N (col4): K opposite H ✅ L left of K ✅ N opposite J ✅ M not at end (col3) ✅ → Opposite I = M ✅
Hint: After placing opposites and adjacency, the remaining non-end person usually occupies the lone middle slot.
Common Mistakes: Placing the non-end person at an end before checking adjacency constraints.
4. Eight persons sit in two rows of four each facing each other. Row-1 (left→right) has M, N, O, P. In Row-2 (left→right) are A, B, C, D. If A is opposite N, B is immediate left of A (bottom-row view), C is opposite O, and D is at the extreme right of Row-2, who is immediate right of B?
medium
A. A
B. C
C. D
D. None

Solution

  1. Step 1: Fix Row-1

    Top row cols1-4 = M, N, O, P.

  2. Step 2: Place A opposite N and C opposite O

    A opposite N → A in bottom col2. C opposite O → C in bottom col3.

  3. Step 3: Place B and D

    B immediate left of A (bottom view) → B in bottom col1. D at extreme right → D in bottom col4. Final bottom row = B, A, C, D.

  4. Step 4: Immediate right of B

    Immediate right of B (col1) is A (col2) → A.

  5. Final Answer:

    A → Option A

  6. Quick Check:

    Bottom row B (col1), A (col2), C (col3), D (col4) gives A opposite N (col2) ✅ B left of A ✅ C opposite O ✅ D at extreme right ✅
Hint: If adjacency and end constraints conflict, place adjacency first then fit ends into remaining slots.
Common Mistakes: Locking end seats too early before placing adjacency clues.
5. Twelve people sit in two rows of six each facing each other. Top row (Row-1 left→right): W, X, Y, Z, U, V. Bottom row (Row-2 left→right) are P, Q, R, S, T, O. If Q is opposite X, R is immediate left of Q (bottom view), S is opposite Z, and P is at extreme right, who is opposite U?
medium
A. O
B. T
C. R
D. P

Solution

  1. Step 1: Fix Row-1 columns

    Cols1-6 (left→right) = W, X, Y, Z, U, V.

  2. Step 2: Place Q opposite X and R left of Q

    Q opposite X → Q in bottom col2. R immediate left of Q (bottom view) → R in bottom col1.

  3. Step 3: Place S opposite Z and P at extreme right

    S opposite Z → S in bottom col4. P at extreme right → P in bottom col6.

  4. Step 4: Fill remaining bottom slots

    Remaining bottom persons T and O occupy col3 and col5. Assign col5 = T and col3 = O. Bottom row = R, Q, O, S, T, P → opposite of U (col5) = T.

  5. Final Answer:

    T → Option B

  6. Quick Check:

    Q opposite X (col2) ✅ R left of Q (col1) ✅ S opposite Z (col4) ✅ P at col6 ✅ → Opposite U (col5) = T ✅
Hint: Place fixed opposites and end seats first; remaining persons fill middle columns.
Common Mistakes: Assuming bottom-row left/right relative to observer rather than each person's facing.

Mock Test

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