Nine employees, K, L, M, N, O, P, Q, R and S, are sitting in the office in a straight line, all facing the east. O is third to the right of M. K is third to the left of P. Q is between P and S. N is fourth to the right of M. P is to the immediate right of N. R is fourth to the left of O. Which of the following statements is NOT correct?
Analyzing the Seating Arrangement Puzzle
This problem involves nine employees sitting in a straight line facing the east. We are given several clues about their relative positions and need to determine the correct seating arrangement to evaluate the given statements.
Step-by-Step Deduction of the Seating Arrangement
Let's use the clues to build the seating arrangement for the nine employees (K, L, M, N, O, P, Q, R, S). Since they are facing east, 'right' means towards the right end of the line and 'left' means towards the left end of the line.
- Clue 5: "P is to the immediate right of N." This gives us the sequence N P.
- Clue 4: "N is fourth to the right of M." If M is at position $x$, N is at position $x+4$.
- Clue 1: "O is third to the right of M." If M is at position $x$, O is at position $x+3$.
Combining clues 1, 4, and 5, we have the relative positions M, O, N, P. Let's assume M is at some position. O is 3rd right, N is 4th right, P is immediate right of N (which is 5th right of M). So the sequence around M is M _ _ O N P.
- Clue 6: "R is fourth to the left of O." If O is at position $y$, R is at position $y-4$. This implies R is to the left of O. Let's try placing R first. If R is at position 1, O is at position $1+4=5$.
Let's combine this with the O N P sequence. If O is at position 5, N is at 6 and P is at 7.
Current partial arrangement (relative positions):
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Employee | R | _ | _ | _ | O | N | P |
Now let's fit M using clue 1: "O is third to the right of M." O is at position 5. M must be at position $5-3=2$. Let's place M at position 2.
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Employee | R | M | _ | _ | O | N | P |
Let's verify clue 4: "N is fourth to the right of M." M is at position 2. N is at position 6. Is 6 the 4th position to the right of 2? $2+4=6$. Yes. This fits.
- Clue 2: "K is third to the left of P." P is at position 7. K must be at position $7-3=4$. Let's place K at position 4.
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Employee | R | M | _ | K | O | N | P |
We have placed R, M, K, O, N, P, which are 6 employees in 7 positions. We need 9 employees. The arrangement so far uses positions 1, 2, 4, 5, 6, 7, leaving position 3 empty. We also need to place L, Q, and S.
- Clue 3: "Q is between P and S." P is at position 7. This means Q and S must be to the right of P, with Q in the middle. Since there are only 2 remaining spots (positions 8 and 9) and 3 people (L, Q, S) to place, and P is already at position 7, Q and S must occupy positions after P. The only way Q can be between P and S is if the sequence is P Q S. So, Q is at position 8 and S is at position 9.
Let's add Q and S to the arrangement:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Employee | R | M | _ | K | O | N | P | Q | S |
We have now used 8 positions and placed 8 employees (R, M, K, O, N, P, Q, S). The remaining employee is L, and the remaining position is 3. Let's place L at position 3.
The final seating arrangement from left to right is:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Employee | R | M | L | K | O | N | P | Q | S |
Let's quickly verify all clues with the final arrangement R M L K O N P Q S:
- O (Pos 5) is 3rd right of M (Pos 2): $2+3=5$. Correct.
- K (Pos 4) is 3rd left of P (Pos 7): $7-3=4$. Correct.
- Q (Pos 8) is between P (Pos 7) and S (Pos 9). Correct.
- N (Pos 6) is 4th right of M (Pos 2): $2+4=6$. Correct.
- P (Pos 7) is immediate right of N (Pos 6). Correct.
- R (Pos 1) is 4th left of O (Pos 5): $5-4=1$. Correct.
All clues are satisfied by the arrangement: R M L K O N P Q S.
Evaluating the Statements
Now let's check each statement based on the final arrangement R M L K O N P Q S.
Statement 1: L is sitting third to the left of O.
O is at position 5. Third to the left of O is position $5-3=2$. The employee at position 2 is M. The statement says L is at this position. This is incorrect.
Statement 2: Q is sitting fourth to the right of K.
K is at position 4. Fourth to the right of K is position $4+4=8$. The employee at position 8 is Q. The statement says Q is at this position. This is correct.
Statement 3: R and S are sitting at the corners.
The corners of the line are positions 1 and 9. R is at position 1 and S is at position 9. The statement says R and S are at the corners. This is correct.
Statement 4: O is sitting between K and N.
K is at position 4, O is at position 5, and N is at position 6. The sequence is K O N. O is indeed sitting between K and N. This is correct.
Identifying the Incorrect Statement
We evaluated each statement based on the deduced seating arrangement R M L K O N P Q S:
- Statement 1: Incorrect
- Statement 2: Correct
- Statement 3: Correct
- Statement 4: Correct
The statement that is NOT correct is Statement 1: L is sitting third to the left of O.
Revision Table: Seating Arrangement
| Clue No. | Clue | Deduction/Placement |
|---|---|---|
| 1 | O is third to the right of M. | Relative position: M _ _ O |
| 2 | K is third to the left of P. | Relative position: K _ _ P |
| 3 | Q is between P and S. | Relative position: P Q S or S Q P (P Q S confirmed later) |
| 4 | N is fourth to the right of M. | Relative position: M _ _ _ N |
| 5 | P is to the immediate right of N. | Relative position: N P |
| 6 | R is fourth to the left of O. | Relative position: R _ _ _ O |
Final Arrangement: R M L K O N P Q S
Additional Information on Seating Arrangement Problems
Seating arrangement problems are common in logical reasoning sections of competitive exams. They test your ability to follow instructions and deduce relationships.
- Always draw a diagram or use a table to represent the seating positions.
- Start with clues that provide fixed positions or strong connections between multiple individuals.
- Combine partial arrangements derived from different clues.
- Keep track of individuals placed and remaining empty spots.
- Verify the final arrangement against all given clues before evaluating the statements.
- Pay close attention to directional words like 'left', 'right', 'immediate left', 'immediate right', and numbers indicating the position difference ('third to the left', 'fourth to the right'). The direction faced by individuals (e.g., East, North, South, West) determines the sense of 'left' and 'right' relative to the diagram.
Important Questions from Linear Arrangement
Eight friends, A, B, C, D, E, F, G and H, are sitting in two lines of four persons each. Both the lines are facing each other. A is facing D. E is to the immediate left of G. H is to the immediate right of B. C is facing G. F is facing H. B is to the immediate right of the person who is facing G. D is to the immediate left of F. Which four persons are sitting in the same line?
Eight north-facing restaurants named P, Q, R, S, T, U, V and W are located in a straight line. S is second to the left of T. W is third to the left of P. T is between P and V. S is third to the left of V. W is to the immediate right of U. R is third to the right of P. Who is sitting fourth to the right of S?
Anamika, Gopal, Nischal, Vanmayi, Shresta and Sripad are sitting in a straight line facing the north. Nischal is to the immediate left of Gopal. Shresta is between Anamika and Sripad. Sripad is at the second place from the right end. Four persons are sitting between Nischal and Vanmayi. If Gopal and Sripad interchange their positions, then who will be sitting between Vanmayi and Shresta?
A question is given, followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and select the appropriate answer.
Question: How many people are standing in the row where all people are facing north?
Statements:
(I) A is fourth from the left end; M is second to the right of A; and R is second from the left end.
(II) M is fourth from the right end; only two people Stand between M and B.
In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statement/s are sufficient to answer the question. Read both the statements and choose your answer carefully.
Question: P, Q, R, S, T, U and V are 7 people standing in a row all facing North (not necessarily in the same order). Who is standing second to the right of T?
Statements:
(I) U is standing 3rd from the right end and 2nd to the left of R.
(II) Q is standing to the immediate right of T. Q is standing 2nd to the left of P
