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: Six people sit in two parallel rows. In Row 1 - J, K and L sit facing towards north, and in Row 2 - F, G and H sit facing towards south. Each person in a row faces a person in the other row. Who faces G? Statements: (I) H faces K; L faces an immediate neighbour of H. (II) G sits at one of the extreme ends of the row; J sits to the immediate left of L.
Data in statements I and II together is sufficient to answer the question
Understanding the Seating Arrangement Problem
This question involves a linear seating arrangement puzzle with six people seated in two parallel rows. Row 1 has J, K, and L facing North. Row 2 has F, G, and H facing South. Each person in Row 1 faces exactly one person in Row 2. We need to determine who among J, K, or L faces G based on the information provided in two statements.
Let's represent the rows and positions. Assuming the seats are numbered P1, P2, and P3 from left to right as viewed by someone facing the row:
- Row 1 (North Facing): P1, P2, P3 (Occupied by J, K, L)
- Row 2 (South Facing): P1, P2, P3 (Occupied by F, G, H)
Since each person in a row faces a person in the other row directly opposite, the facing pairs are:
- P1 in Row 1 faces P1 in Row 2
- P2 in Row 1 faces P2 in Row 2
- P3 in Row 1 faces P3 in Row 2
Analyzing Statement I for Seating Positions
Statement I gives us two pieces of information:
- H faces K.
- L faces an immediate neighbour of H.
From point 1, since H is in Row 2 and K is in Row 1 and they face each other, they must be in the same position number. So, K and H are either both at P1, both at P2, or both at P3.
- If K is at P1(R1), then H is at P1(R2). The immediate neighbour of H in Row 2 is P2(R2). L faces a neighbour of H, so L faces P2(R2). This means L must be at P2(R1).
- If K is at P2(R1), then H is at P2(R2). The immediate neighbours of H in Row 2 are P1(R2) and P3(R2). L faces a neighbour of H, so L faces either P1(R2) or P3(R2). This means L is either at P1(R1) or P3(R1).
- If K is at P3(R1), then H is at P3(R2). The immediate neighbour of H in Row 2 is P2(R2). L faces a neighbour of H, so L faces P2(R2). This means L must be at P2(R1).
Let's see the possible arrangements in Row 1 (J, K, L) based on these conditions:
- Case 1: K is P1(R1), L is P2(R1). The remaining person J must be P3(R1). Row 1: K L J. Row 2: H P2 P3 (H=P1 R2).
- Case 2: K is P2(R1), L is P1(R1). The remaining person J must be P3(R1). Row 1: L K J. Row 2: P1 H P3 (H=P2 R2).
- Case 3: K is P2(R1), L is P3(R1). The remaining person J must be P1(R1). Row 1: J K L. Row 2: P1 H P3 (H=P2 R2).
- Case 4: K is P3(R1), L is P2(R1). The remaining person J must be P1(R1). Row 1: J L K. Row 2: P1 P2 H (H=P3 R2).
Now, let's place F and G in Row 2 ({F, G, H}).
In Case 1: Row 1 is K L J. Row 2 is H P2 P3. {P2, P3} = {F, G}. L (P2 R1) faces P2(R2). P2(R2) is a neighbour of H (P1 R2). This is true. If P2(R2) is G, then G faces L. If P2(R2) is F, then G must be P3(R2), and G faces J. So, G can be faced by L or J.
In Case 2: Row 1 is L K J. Row 2 is P1 H P3. {P1, P3} = {F, G}. L (P1 R1) faces P1(R2). P1(R2) must be a neighbour of H (P2 R2). This is true. If P1(R2) is G, then G faces L. If P1(R2) is F, then G must be P3(R2), and G faces J. So, G can be faced by L or J.
In Case 3: Row 1 is J K L. Row 2 is P1 H P3. {P1, P3} = {F, G}. L (P3 R1) faces P3(R2). P3(R2) must be a neighbour of H (P2 R2). This is true. If P3(R2) is G, then G faces L. If P3(R2) is F, then G must be P1(R2), and G faces J. So, G can be faced by L or J.
In Case 4: Row 1 is J L K. Row 2 is P1 P2 H. {P1, P2} = {F, G}. L (P2 R1) faces P2(R2). P2(R2) must be a neighbour of H (P3 R2). This is true. If P2(R2) is G, then G faces L. If P2(R2) is F, then G must be P1(R2), and G faces J. So, G can be faced by L or J.
Statement I alone gives multiple possibilities for who faces G. Therefore, statement I alone is insufficient.
Analyzing Statement II for Seating Positions
Statement II gives us two pieces of information:
- G sits at one of the extreme ends of the row.
- J sits to the immediate left of L.
From point 1, G is in Row 2 and is at an extreme end. So, G is either at P1(R2) or P3(R2).
From point 2, J sits immediately to the left of L in Row 1 (North facing). In a North-facing row with seats P1, P2, P3 from left to right, "immediate left" means the person is in the seat position immediately before L. So, if L is at P2(R1), J is at P1(R1). If L is at P3(R1), J is at P2(R1). L cannot be at P1(R1) as there's no seat to its left.
Possible arrangements for Row 1 (J, K, L) based on J being immediately left of L:
- If L is at P2(R1), J is at P1(R1). The remaining person K must be at P3(R1). Row 1: J L K.
- If L is at P3(R1), J is at P2(R1). The remaining person K must be at P1(R1). Row 1: K J L.
Let's consider these Row 1 arrangements with G at an end in Row 2 ({F, G, H}).
If Row 1 is J L K (J=P1, L=P2, K=P3):
- If G is at P1(R2), then J faces G. Row 2 could be G F H or G H F. J faces G in both cases. K faces H or F, L faces F or H.
- If G is at P3(R2), then K faces G. Row 2 could be F H G or H F G. K faces G in both cases. J faces F or H, L faces H or F.
In this scenario (Row 1 is J L K), G can be faced by J or K, depending on G's position in Row 2.
If Row 1 is K J L (K=P1, J=P2, L=P3):
- If G is at P1(R2), then K faces G. Row 2 could be G F H or G H F. K faces G in both cases. J faces F or H, L faces H or F.
- If G is at P3(R2), then L faces G. Row 2 could be F H G or H F G. L faces G in both cases. K faces F or H, J faces H or F.
In this scenario (Row 1 is K J L), G can be faced by K or L, depending on G's position in Row 2.
Statement II alone gives multiple possibilities for who faces G. Therefore, statement II alone is insufficient.
Combining Statement I and Statement II
Now we use information from both statements. From Statement II, the arrangement in Row 1 must be either J L K or K J L.
Case A: Row 1 is J L K (J=P1, L=P2, K=P3). From Statement I, K and H are in the same position. Since K is at P3(R1), H must be at P3(R2). Row 1: J(P1) L(P2) K(P3) Row 2: P1 P2 H(P3) The remaining people in Row 2 are F and G, so {P1(R2), P2(R2)} = {F, G}. From Statement I, L faces an immediate neighbour of H. L is at P2(R1) and faces P2(R2). H is at P3(R2). The immediate neighbour of H (at P3 R2) in Row 2 is P2(R2). The condition says L faces a neighbour of H, which means P2(R2) must be a neighbour of P3(R2). This is true in a three-seat linear row. From Statement II, G is at an extreme end (P1 or P3) in Row 2. In Row 2 (P1 P2 H), the ends are P1 and P3. H is at P3. Since G is not H, G must be at P1(R2). Row 2: G(P1) P2(R2) H(P3). Since {P1(R2), P2(R2)} = {F, G} and G is at P1(R2), F must be at P2(R2). Row 2: G(P1) F(P2) H(P3). Let's check if this arrangement satisfies all conditions:
- Row 1: J L K (North), Row 2: G F H (South). People are correct.
- St I: H faces K. K=P3(R1), H=P3(R2). Correct. L faces neighbour of H. L=P2(R1) faces F=P2(R2). F is the neighbour of H (at P3 R2). Correct.
- St II: G is at extreme end. G is at P1(R2). Correct. J sits immediate left of L. In J L K, J is left of L. Correct.
This arrangement is valid. In this arrangement, J (P1 R1) faces G (P1 R2).
| Row | P1 | P2 | P3 |
|---|---|---|---|
| Row 1 (North) | J | L | K |
| Row 2 (South) | G | F | H |
Case B: Row 1 is K J L (K=P1, J=P2, L=P3). From Statement I, K and H are in the same position. Since K is at P1(R1), H must be at P1(R2). Row 1: K(P1) J(P2) L(P3) Row 2: H(P1) P2 P3 The remaining people in Row 2 are F and G, so {P2(R2), P3(R2)} = {F, G}. From Statement I, L faces an immediate neighbour of H. L is at P3(R1) and faces P3(R2). H is at P1(R2). The immediate neighbour of H (at P1 R2) in Row 2 is P2(R2). The condition says L faces a neighbour of H, which means P3(R2) must be a neighbour of P1(R2). This is false in a three-seat linear row (P1 and P3 are not neighbours). This arrangement contradicts Statement I.
Therefore, only Case A is valid when combining both statements. In Case A, the arrangement is Row 1: J L K and Row 2: G F H. In this arrangement, J faces G.
Conclusion on Data Sufficiency
Statement I alone is insufficient as it leads to multiple possibilities for who faces G (L or J). Statement II alone is insufficient as it also leads to multiple possibilities (J, K, or L could face G). However, when we combine the information from both statements, we arrive at a single, unique seating arrangement that satisfies all the given conditions. In this unique arrangement, J faces G. Therefore, the data in statements I and II together is sufficient to answer the question.
The question "Who faces G?" can be definitively answered as J using both statements together.
Revision Table - Seating Arrangement Analysis
| Statement(s) Used | Sufficiency | Explanation |
|---|---|---|
| Statement I Alone | Insufficient | Leads to G being faced by L or J depending on specific arrangements. |
| Statement II Alone | Insufficient | Restricts Row 1 arrangement and G's position in Row 2 (end), but multiple possibilities for who faces G remain. |
| Statements I and II Together | Sufficient | Only one arrangement satisfies all conditions, uniquely identifying the person facing G as J. |
Additional Information - Parallel Row Seating Puzzles
Parallel row seating arrangement puzzles are common in logical reasoning sections of exams. Key concepts to remember include:
- Relative Positioning: Understand terms like "left", "right", "immediate left", "immediate right" based on the direction the person is facing.
- Facing Positions: In parallel rows where people face each other, the person at a certain position number in one row faces the person at the corresponding position number in the other row (e.g., P1 faces P1, P2 faces P2).
- Neighbours: Immediate neighbours are the persons seated next to someone in the same row.
- Extreme Ends: These are the seats at the beginning and end of a row (P1 and P3 in a 3-seat row).
- Data Sufficiency: To be sufficient, the given data must lead to one and only one possible answer to the question asked. If multiple possibilities exist, the data is insufficient.
Solving these puzzles often requires drawing diagrams or tables to represent the arrangements and systematically testing the given conditions. Start with the most restrictive conditions first.
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Important Questions from Linear Arrangement
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How many people sit between R and V?
