Three boys T, R and M are sitting in a row facing towards the north (not necessarily in the same order), and three girls F, G and K are sitting in a row facing towards the face of these boys (not necessarily in the same order). F and R are diagonally opposite to each other. K is not at any of the ends. Which of the following pairs of persons facing towards each other is/are definitely correct? I. GR II. KT
Only I
Solving Seating Arrangement Puzzles
This question involves a linear seating arrangement puzzle with two rows facing each other. We have three boys (T, R, M) in one row facing North and three girls (F, G, K) in another row facing South, towards the boys. The two rows are positioned such that individuals directly opposite each other are in the same column.
Understanding the Seating Setup
Let's visualize the two rows. Since the boys face North and girls face South towards the boys, they are essentially in parallel rows, one above the other. Let's represent the positions in each row from left to right (from the perspective of someone looking at the row):
Girls' Row (Facing South): Position 1, Position 2, Position 3
Boys' Row (Facing North): Position 1, Position 2, Position 3
An individual at Position 1 in the girls' row faces the individual at Position 1 in the boys' row, and similarly for Positions 2 and 3.
| Girls' Row (Facing South) | Facing | Boys' Row (Facing North) |
|---|---|---|
| Position 1 | <--> | Position 1 |
| Position 2 | <--> | Position 2 |
| Position 3 | <--> | Position 3 |
Applying the Clues in the Seating Arrangement
We are given two main clues:
- K is not at any of the ends.
- F and R are diagonally opposite to each other.
Clue 1: K's Position
If K is not at any of the ends in the girls' row (which has 3 positions), K must be in the middle position. So, K is at Position 2 in the girls' row.
| Girls' Row (Facing South) | Facing | Boys' Row (Facing North) |
|---|---|---|
| _ | <--> | _ |
| K (Position 2) | <--> | _ (Position 2) |
| _ | <--> | _ |
Clue 2: F and R are Diagonally Opposite
Diagonally opposite means they are in different rows and different end positions. For a 3x3 setup like this (considering positions), the diagonal pairs are (Girl P1, Boy P3) and (Girl P3, Boy P1).
Since K is at Girl P2, F cannot be at Girl P2. F must be at either Girl P1 or Girl P3. Correspondingly, R must be at the diagonally opposite end in the boys' row.
This gives us two possible scenarios for F and R:
- F is at Girl Position 1, and R is at Boy Position 3.
- F is at Girl Position 3, and R is at Boy Position 1.
Scenario 1: F at Girl P1, R at Boy P3
If F is at Girl Position 1, K is at Girl Position 2 (from Clue 1), then the remaining girl, G, must be at Girl Position 3. If R is at Boy Position 3, the remaining boys (T and M) must occupy Boy Positions 1 and 2.
| Girls' Row (Facing South) | Facing | Boys' Row (Facing North) |
|---|---|---|
| F (Position 1) | <--> | _ (Position 1) - T or M |
| K (Position 2) | <--> | _ (Position 2) - T or M |
| G (Position 3) | <--> | R (Position 3) |
In this scenario, the pairs facing each other are:
- F faces either T or M.
- K faces either T or M.
- G faces R.
Scenario 2: F at Girl P3, R at Boy P1
If F is at Girl Position 3, K is at Girl Position 2, then G must be at Girl Position 1. If R is at Boy Position 1, the remaining boys (T and M) must occupy Boy Positions 2 and 3.
| Girls' Row (Facing South) | Facing | Boys' Row (Facing North) |
|---|---|---|
| G (Position 1) | <--> | R (Position 1) |
| K (Position 2) | <--> | _ (Position 2) - T or M |
| F (Position 3) | <--> | _ (Position 3) - T or M |
In this scenario, the pairs facing each other are:
- G faces R.
- K faces either T or M.
- F faces either T or M.
Analyzing the Statements
Now let's check which of the given statements about facing pairs is definitely correct based on these two scenarios.
Statement I: G R
- In Scenario 1, G is at Girl P3 and R is at Boy P3. They face each other.
- In Scenario 2, G is at Girl P1 and R is at Boy P1. They face each other.
In both possible scenarios, G and R are in positions that face each other. Therefore, the pair G R is definitely facing each other.
Statement II: K T
- In Scenario 1, K is at Girl P2. The boy at Boy P2 could be either T or M. So, K could face T, or K could face M.
- In Scenario 2, K is at Girl P2. The boy at Boy P2 could be either T or M. So, K could face T, or K could face M.
In neither scenario is it guaranteed that T is the boy facing K. K might face M. Therefore, the pair K T is not definitely facing each other.
Conclusion on Definitely Correct Pairs
Based on the analysis of both possible seating arrangements derived from the clues, only Statement I (G R) is definitely correct. Statement II (K T) is not definitely correct as K could face M instead of T.
Revision Table: Key Information
| Concept | Details |
|---|---|
| Seating Type | Two rows facing each other (Linear Arrangement) |
| Number of People | 3 Boys (T, R, M), 3 Girls (F, G, K) |
| Row Direction | Boys North, Girls South |
| K's Position | Middle (Position 2 in girls' row) |
| F & R Relation | Diagonally Opposite Ends |
| Scenario 1 Outcome | G faces R, K faces T/M, F faces T/M |
| Scenario 2 Outcome | G faces R, K faces T/M, F faces T/M |
| Definitely Correct Pair | G faces R (Consistent in both scenarios) |
Additional Information: Seating Arrangement Strategies
Seating arrangement problems are common in logical reasoning tests. Here are some general strategies to tackle them effectively:
- Visualize or Draw: Always draw the setup. For linear arrangements, draw rows and positions. For circular, draw a circle.
- Note Clues: Write down each clue separately.
- Identify Fixed Positions: Start with clues that fix someone's position directly (like K not being at ends).
- Identify Relative Positions: Use clues that describe positions relative to others (like F and R being diagonally opposite).
- Handle 'Not' Clues: Clues like "is not at an end" or "is not next to" help eliminate possibilities.
- Consider All Scenarios: If a clue leads to multiple possibilities (like F and R), explore each scenario separately until it contradicts another clue or you find what is definitely true across all valid scenarios.
- Check Statements Against Scenarios: For "definitely correct" or "possibly true" questions, test each statement against every valid scenario you've created.
- Elimination: Use the options provided to guide your analysis or eliminate invalid arrangements.
Important Questions from Linear Arrangement
- Five people (A, B, C, D and E) are sitting in a straight line. They all are facing towards the north. B is sitting immediately between C and E. A is sitting third to the left of E. C is sitting second to the right of D. Who is sitting at the extreme left end of line?
- Six people A, B, C, D, E and F are sitting in a straight line. All are facing towards North.
B is seated third from the extreme right end of the line.
Only two people are seated between B and E.
C is sitting second from the right of B.
F is an immediate neighbour of B and C.
A is sitting to the immediate right of D.
How many people are seated between D and F? - Seven people A, B, C, D, E, F and G are sitting in a row, facing the north. Only three people sit to the left of D. B sits third to the left of D. F sits to the right of A but left of D. E sits to the right of C but left of G. How many people sit to the right of F?
- Seven people, I, J, K, L, M, N and O, are sitting in a row, facing north. Only three people sit to the left of M. Only I sits to the right of O. Only three people sit between O and N. J sits at some place to the left of K but at some place to the right of L. How many people sit between L and K?
- Seven people A, B, C, D, E, F and G are sitting in a row, facing north. Only two people sit between D and C. Only G sits to the right of E. Only one person sits between C and E. A sits at some place to the right of F but at some place to the left of B. How many people sit to the right of A?
