Question Details

Read the given information carefully and answer the questions based on it:

Eight persons sit in a row. Four persons face north and rest face south. Three persons sit between A and B and one of them sits at the end of the row. C sits second to the right of B who faces north. D and B face same direction but they do not sit adjacent to each other. E sits third to the left of D and faces opposite direction to D. G sits third to the right of C. Both the immediate neighbors of G face same direction. H sits to the right of F.

What is the position of F with respect to E?

Options

A

Second to the right

B

Second to the left

C

Fourth to the left

D

Third to the right

Show Answer

Correct Answer :

Option C

Fourth to the left

Fourth to the left

Solution :

To find the position of F with respect to E, we will step-by-step reconstruct the seating arrangement of the eight persons in the row based on the given clues.

Let the eight positions in the row be numbered 1 to 8 from left to right.
Clue 1: "Three persons sit between A and B and one of them sits at the end of the row."
This means either A or B sits at one of the ends (position 1 or 8). Since three persons sit between them, the distance between their positions is 4. Thus, the possible pairs of positions for {A, B} are:
Case 1: B is at position 1, A is at position 5.
Case 2: B is at position 8, A is at position 4.
Case 3: A is at position 1, B is at position 5.
Case 4: A is at position 8, B is at position 4.

Clue 2: "C sits second to the right of B who faces north."
Since B faces north (facing upwards):
- If B is at position 1 (Case 1), C (second to the right of B) must be at position 3.
- If B is at position 8 (Case 2), C cannot sit second to the right of B because position 10 does not exist. So, Case 2 is eliminated.
- If B is at position 5 (Case 3), C must be at position 7.
- If B is at position 4 (Case 4), C must be at position 6.
This leaves us with Case 1, Case 3, and Case 4.

Clue 3: "G sits third to the right of C."
Let us evaluate G's position for our remaining cases:
- Case 1 (B=1, A=5, C=3): If C faces north, G (third to the right) is at position 6. If C faces south, G (third to the right, which is to the left in row coordinates) is at position 0, which is invalid. Thus, C must face north, and G is at position 6.
- Case 3 (A=1, B=5, C=7): If C faces north, G would be at position 10 (invalid). If C faces south, G is at position 4. Thus, C must face south, and G is at position 4.
- Case 4 (A=8, B=4, C=6): If C faces north, G would be at position 9 (invalid). If C faces south, G is at position 3. Thus, C must face south, and G is at position 3.

Clue 4: "E sits third to the left of D and faces opposite direction to D. D and B face same direction but they do not sit adjacent to each other."
Since B faces north, D also faces north.
Since D faces north, E (third to the left of D) must be 3 positions to the left of D. That is, E=D-3.
Also, D and B cannot sit adjacent to each other.
Let's test this in the remaining cases:
- Case 1 (B=1, A=5, C=3, G=6):
The vacant positions are 2, 4, 7, 8.
Since E=D-3, the possible pairs for (E, D) are:
- If D = 7, then E = 4. (Both 4 and 7 are vacant. Since B=1, D=7 is not adjacent to B. This is valid).
- If D = 8, then E = 5. But position 5 is occupied by A.
Thus, in Case 1, E is at position 4 and D is at position 7 (facing north). Since E faces the opposite direction to D, E faces south.
The remaining positions to be filled are 2 and 8. The remaining persons are F and H.
- Case 3 (A=1, B=5, C=7, G=4):
The vacant positions are 2, 3, 6, 8.
For E=D-3:
- If D = 6, then E = 3 (both vacant). But D=6 is adjacent to B=5, which is invalid.
- If D = 8, then E = 5, but position 5 is occupied by B.
So, Case 3 is eliminated.
- Case 4 (A=8, B=4, C=6, G=3):
The vacant positions are 1, 2, 5, 7.
For E=D-3:
- If D = 5, E = 2. But D=5 is adjacent to B=4, which is invalid.
- If D = 8, position 8 is occupied.
So, Case 4 is eliminated.

Therefore, only Case 1 is valid:
Seating positions:
1: B (faces North)
2: Vacant (F or H)
3: C (faces North)
4: E (faces South)
5: A
6: G
7: D (faces North)
8: Vacant (F or H)

Clue 5: "Both the immediate neighbors of G face same direction."
The immediate neighbors of G (at position 6) are A (at position 5) and D (at position 7).
Since D faces north, A must also face north.

Clue 6: "H sits to the right of F."
The remaining positions for F and H are 2 and 8.
If F is at 8 and H is at 2:
For H to sit to the right of F, F must face south (so that his right is towards position 1).
If F is at 2 and H is at 8:
For H to sit to the right of F, F must face north (so that his right is towards position 8).
Let us check the number of directions: "Four persons face north and rest face south."
We currently know the directions of:
- B: North
- C: North
- D: North
- E: South
- A: North
Since four persons face north (B, C, D, A), the remaining four persons (E, G, F, H) must face south.
Since F faces south, F must be at position 8 and H must be at position 2. Let's verify: H (at position 2) is indeed to the right of F (at position 8 facing south).
This perfectly matches all conditions.

Final Seating Arrangement:
1: B (North)
2: H (South)
3: C (North)
4: E (South)
5: A (North)
6: G (South)
7: D (North)
8: F (South)

Finding the position of F with respect to E:
E is at position 4 and faces south.
Since E faces south, the direction to E's left is to the right of the row (towards position 8).
F is at position 8, which is 8-4=4 positions to the left of E.
Therefore, F is Fourth to the left of E.

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