Six persons P, Q, R, S, T and U are sitting in a straight line, all facing in the same direction. Q is to the immediate left of P. R is second from the right end. Q is third to the left of R. T is third to the left of S. What is U’s position in the line?
Solving the Linear Arrangement Puzzle
This question asks us to determine the position of person U in a linear arrangement involving six persons: P, Q, R, S, T, and U. All persons are facing the same direction in a straight line. We are given several clues to help us deduce the seating arrangement.
Analyzing the Clues for the Linear Arrangement
Let's break down the given clues about the positions of the six persons:
- Clue 1: Q is to the immediate left of P. This tells us that Q and P are sitting next to each other in that specific order: Q P.
- Clue 2: R is second from the right end. In a line of six persons, the positions can be numbered 1 to 6 from left to right (or right to left, consistency is key). If we number from the left, the right end is position 6. Second from the right means position 5. So, R is at position 5.
- Clue 3: Q is third to the left of R. Since R is at position 5 (assuming numbering from left), Q is at position \(5 - 3 = 2\). So, Q is at position 2.
- Clue 4: T is third to the left of S.
Step-by-Step Deduction of the Seating Arrangement
Let's use the clues to build the arrangement step by step for the six persons. Let the positions be numbered 1, 2, 3, 4, 5, 6 from left to right.
From Clue 2, R is second from the right end, placing R at position 5:
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 |
|---|---|---|---|---|---|
| R |
From Clue 3, Q is third to the left of R (at position 5). This places Q at position \(5 - 3 = 2\):
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 |
|---|---|---|---|---|---|
| Q | R |
From Clue 1, Q is to the immediate left of P. Since Q is at position 2, P must be at position 3:
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 |
|---|---|---|---|---|---|
| Q | P | R |
Now, we have positions 1, 4, and 6 remaining. The persons T and S need to be placed such that T is third to the left of S (Clue 4). Let's examine the possible pairs of empty positions where this relationship can hold:
- If S is at position 4, T would be at position \(4 - 3 = 1\). Positions 1 and 4 are both empty. This is a valid placement.
- If S is at position 6, T would be at position \(6 - 3 = 3\). Position 3 is already occupied by P. This is not a valid placement.
Therefore, T must be at position 1 and S at position 4:
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 |
|---|---|---|---|---|---|
| T | Q | P | S | R |
We have now placed five of the six persons (T, Q, P, S, R). The only remaining person is U, and the only remaining empty position is position 6.
So, U must be at position 6.
| Position 1 | Position 2 | Position 3 | Position 4 | Position 5 | Position 6 |
|---|---|---|---|---|---|
| T | Q | P | S | R | U |
Determining U’s Position in the Line
The final arrangement from left to right is T, Q, P, S, R, U.
U is at position 6, which is the rightmost position.
Let's look at the options and see which one accurately describes U's position:
- Between Q and S: Q is at position 2, S is at position 4. P is between Q and S. U is at position 6, which is not between Q and S. This option is incorrect.
- To the immediate right of R: R is at position 5. U is at position 6, which is immediately to the right of position 5. This option is correct.
- To the immediate right of P: P is at position 3. S is at position 4, which is immediately to the right of P. U is at position 6. This option is incorrect.
- To the immediate left of S: S is at position 4. P is at position 3, which is immediately to the left of S. U is at position 6. This option is incorrect.
Based on our step-by-step deduction of the linear arrangement, U is at position 6, which is immediately to the right of R (at position 5).
Revision Table: Linear Arrangement Key Concepts
| Concept | Explanation | Application in Puzzle |
|---|---|---|
| Linear Arrangement | Arranging items/persons in a straight line. | Six persons arranged in a single row. |
| Relative Position | Position of an item/person with respect to others (e.g., 'left of', 'right of', 'between'). | Q is immediate left of P, Q is third left of R, T is third left of S. |
| End Positions | The positions at either extremity of the line (leftmost, rightmost). | R is second from the right end (position 5 in a 6-person line from left). U is at the rightmost end (position 6). |
Additional Information: Solving Seating Arrangement Puzzles
Seating arrangement questions are common in logical reasoning sections of many exams. They require you to use given clues to deduce the order or position of individuals or objects in a linear, circular, square, or other formation.
Tips for Solving Linear Arrangement Puzzles:
- Always start with the most definitive information, such as someone's position relative to an end (like R being second from the right).
- For relative positions (like 'left of', 'right of'), maintain consistency in numbering or visualizing positions (e.g., always number from left to right).
- Combine clues step by step. Use each piece of information to narrow down the possibilities and fill in positions in your diagram or table.
- Look for clues that link different individuals together (like Q and P being immediate neighbours).
- Keep track of the individuals who have been placed and the positions that are still empty.
- If a clue gives a position relative to someone whose exact position isn't yet known, mark it down and come back to it once that person's position is determined.
- Cross-reference all clues to ensure your deduced arrangement satisfies every condition given in the problem.
Practicing different types of arrangement problems will help improve your speed and accuracy in solving them.
Similar Questions
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Important Questions from Linear Arrangement
Seven people, A, B, C, D, E, F and G, are sitting in a straight row facing the north. Only two people sit to the left of C. Only two people sit between A and B. B sits to the left of A. E is an immediate neighbour of A to the right. Only one person sits to the right of D. F is not an immediate neighbour of B. Who sits at the centre?
P, Q, R and S are sitting on a bench and facing in the same direction. P sits next to Q but not next to R. S, who is sitting on the extreme right, does not sit next to either Q or R. How many of them each have two neighbors?
5 boys A, B, C, D and E are sitting in a row. E is sitting between D and A, B is to the right of A, C is at one of the extreme ends and C and D are sitting next to each other. Which of the following statement is false?
Five friends Ram, Priya, Raunak, Aditya and Shyam are sitting in a row facing north. Raunak is to the right of Shyam and Priya is to the left of Shyam but to the right of Rama. Raunak is to the left of Aditya. Who is fourth from the left end?
Seven friends P, Q, R, S, T, U, and V are sitting in a straight line facing north. Q sits fifth to the right of T. Q does not sit at any of the extreme ends. Two people sit between U and R. S sits third to the left of V. S sits exactly in the middle. U is not an immediate neighbour of P.
How many people sit between R and V?
