Seven friends K, L, M, N, O, P and Q are sitting in a straight line. Only Q is between P and L. K is second from the right end. Two friends are sitting between M and O. M is at one of the ends. P is third from the left end and is to the immediate left of O. K is not sitting adjacent to O. Who is sitting at the third place from the right end?
N
Solving the Seating Arrangement Puzzle
This question asks us to determine the position of friends sitting in a straight line based on several clues. We need to carefully analyze each piece of information to build the final arrangement.
Understanding the Clues for Seating Arrangement
Let's break down the given statements one by one:
- There are seven friends: K, L, M, N, O, P, and Q.
- They are sitting in a straight line. We can imagine 7 positions from left to right.
- Clue 1: Only Q is between P and L. This suggests a block like P-Q-L or L-Q-P.
- Clue 2: K is second from the right end. If we number positions 1 to 7 from left to right, K is at position 6 (from the left end).
- Clue 3: Two friends are sitting between M and O.
- Clue 4: M is at one of the ends. M can be at position 1 (left end) or position 7 (right end).
- Clue 5: P is third from the left end. P is at position 3.
- Clue 6: P is to the immediate left of O. This means O is at position 4.
- Clue 7: K is not sitting adjacent to O. Since O is at position 4, K cannot be at position 3 or 5. We already know K is at position 6, so this clue is consistent with clue 2.
Building the Seating Arrangement Step-by-Step
Let's use the concrete positions we found first:
Based on Clue 5, P is at position 3:
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 | Position 7 |
|---|---|---|---|---|---|---|
| P |
Based on Clue 6, P is to the immediate left of O. So O is at position 4:
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 | Position 7 |
|---|---|---|---|---|---|---|
| P | O |
Based on Clue 2, K is second from the right end (position 6):
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 | Position 7 |
|---|---|---|---|---|---|---|
| P | O | K |
Based on Clue 1, only Q is between P and L. Since P is at position 3 and O is at position 4, the sequence P-Q-L must start at or before position 3. If P is at 3, then Q must be at 2 and L at 1. This fits the pattern and available spots.
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 | Position 7 |
|---|---|---|---|---|---|---|
| L | Q | P | O | K |
Based on Clue 4, M is at one of the ends. The ends are position 1 and position 7. Position 1 is occupied by L. So, M must be at position 7.
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 | Position 7 |
|---|---|---|---|---|---|---|
| L | Q | P | O | K | M |
Now let's check Clue 3: Two friends are sitting between M and O. M is at position 7, O is at position 4. The friends between them are at positions 5 and 6 (K and the empty spot). This fits the clue.
We have one friend left (N) and one empty spot (position 5). So, N must be at position 5.
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 | Position 7 |
|---|---|---|---|---|---|---|
| L | Q | P | O | N | K | M |
Let's quickly verify all clues with the final arrangement:
- Only Q is between P (Pos 3) and L (Pos 1)? No, this implies the sequence is L-Q-P or P-Q-L. Our arrangement is L-Q-P at the start. Q is between L and P. This clue might be interpreted as "Q is the only person directly between P and L in their relative order". In our case, L is at 1, Q at 2, P at 3. Q is indeed between L and P, and no one else is *directly* between them. Let's re-read. "Only Q is between P and L". This usually means P-Q-L or L-Q-P. If P is at 3 and O is at 4 (P immediate left of O), then P-Q-L sequence must be at 1-2-3 positions (L-Q-P) or 3-4-5 (P-Q-L). Since P is at 3, P-Q-L at 3-4-5 is impossible as O is at 4. So it must be L-Q-P at 1-2-3. This works.
- K is second from the right end (Position 6): Yes.
- Two friends are sitting between M (Pos 7) and O (Pos 4)? Yes, N (Pos 5) and K (Pos 6) are between them.
- M is at one of the ends (Pos 7): Yes.
- P is third from the left end (Pos 3): Yes.
- P is to the immediate left of O (Pos 3 is left of Pos 4): Yes.
- K is not sitting adjacent to O (K is at 6, O is at 4): Yes, they are not adjacent.
All clues are satisfied by the arrangement: L Q P O N K M.
Identifying the Third Person from the Right End
The line is L Q P O N K M.
Counting from the right end (M):
- First from right: M (Position 7)
- Second from right: K (Position 6)
- Third from right: N (Position 5)
The person sitting at the third place from the right end is N.
Final Seating Arrangement
| Position 1 (Left End) |
Position 2 | Position 3 | Position 4 | Position 5 (3rd from Right) |
Position 6 (2nd from Right) |
Position 7 (Right End) |
|---|---|---|---|---|---|---|
| L | Q | P | O | N | K | M |
Therefore, N is sitting at the third place from the right end.
Revision Table: Key Seating Arrangement Clues
| Clue | Deduction | Position(s) |
|---|---|---|
| 7 friends in a line | 7 positions | 1 to 7 |
| P is 3rd from left | P is at Position 3 | Pos 3: P |
| P is immediate left of O | O is at Position 4 | Pos 4: O |
| Only Q is between P and L | Sequence P-Q-L or L-Q-P | Given P=3, O=4, only L-Q-P at 1-2-3 works |
| K is 2nd from right | K is at Position 6 | Pos 6: K |
| M is at an end | M is at Pos 1 or Pos 7 | Pos 1 is L, so M must be at Pos 7 |
| Two friends between M and O | Positions 5 & 6 must be between Pos 4 & 7 | Consistent with K at 6 and N deduced at 5 |
| K not adjacent to O | K cannot be at 3 or 5 (O is at 4) | K is at 6, consistent |
| Remaining friend N fills remaining spot | N is at Position 5 | Pos 5: N |
| Third from right end | Count 3 spots from Pos 7 | Position 5 |
Additional Information on Linear Arrangements
Linear arrangement questions are common in reasoning tests. They involve placing people or objects in a straight line based on given conditions. Here are some tips for solving them:
- Always start with the most concrete information, like someone being at a specific numbered position or at an end.
- Look for clues that link multiple people together, like "X is between Y and Z" or "A is to the immediate left of B". These create blocks that can be placed.
- Use diagrams or draw lines to represent the positions. Write down the names as you confirm their spots.
- Keep track of the people who have been placed and the remaining empty spots.
- Check all the original clues against your final arrangement to ensure consistency.
- Pay attention to wording like "immediate left/right" versus simply "left/right" (which can mean anywhere on that side).
- "Between X and Y" can sometimes mean only X_Y, or it can mean there are people only between X and Y. Context is key. In this case, "Only Q is between P and L" means the sequence is specifically P-Q-L or L-Q-P with nothing else in between those three.
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?
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?
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.
