Question Details

Analyze the given information thoroughly and answer the following question.


Eight students, A, B, C, D, E, F, G, and H, sit in a row such that some face North and others face South. No three consecutive students face the same direction. A sits at the extreme left end of the row. F sits second to the left of H, who faces North. Four students sit between B and G, and G faces North. D sits second to the right of B. C sits adjacent to B and faces South. E sits to the immediate right of F.

How many students face the south direction?

Options

A

Five

B

None of these

C

Four

D

Two

E

Three

Show Answer

Correct Answer :

Option C

Four

Solution :

The correct answer is Four.

Step 1: Determine the seating positions from left to right (Positions 1 to 8)
Let the eight positions in a row from left to right be numbered 1, 2, 3, 4, 5, 6, 7, and 8.
1. A's Position: "A sits at the extreme left end of the row."
⇒ Position 1 = A.
2. B and G's Positions: "Four students sit between B and G, and G faces North."
The possible pairs of positions with 4 students between them are (1, 6), (2, 7), and (3, 8). Since Position 1 is occupied by A, B and G must occupy either (2, 7) or (3, 8).
3. D's Position: "D sits second to the right of B."
- If B were at Position 3 facing South, 2nd to the right of B would be Position 1 (which is A, impossible).
- If B were at Position 7, 2nd to the right of B would be outside the row or conflict.
- Therefore, B must be at Position 2 facing North.
- Since B is at Position 2 and faces North, 2nd to the right of B is Position 4 = D.
- Since B is at Position 2, Position 7 = G (facing North).
4. C's Position: "C sits adjacent to B and faces South."
The positions adjacent to B (Position 2) are Position 1 (occupied by A) and Position 3. Thus, Position 3 = C (facing South).
5. H and F's Positions: "F sits second to the left of H, who faces North."
Since H faces North, "left of H" means moving towards the left (lower position numbers).
The available remaining positions are 5, 6, and 8.
Placing Position 8 = H (facing North) puts 2nd to the left of H at Position 6 = F.
6. E's Position: "E sits to the immediate right of F."
With F at Position 6, the remaining position is Position 5 = E.
For E (Position 5) to be to the immediate right of F (Position 6), F must face South.

Step 2: Summary of Seating Arrangement
- Position 1: A
- Position 2: B (North)
- Position 3: C (South)
- Position 4: D
- Position 5: E
- Position 6: F (South)
- Position 7: G (North)
- Position 8: H (North)

Step 3: Determine the Facing Directions
Rule: "No three consecutive students face the same direction."
- Positions 7 and 8 both face North. Since Position 6 (F) faces South, the condition of no three consecutive students facing North is satisfied at the right end.
- Out of the 8 students, C (Position 3) and F (Position 6) definitely face South, while B (Position 2), G (Position 7), and H (Position 8) face North.
- Applying the rule to the remaining positions (A, D, and E) without forming any group of three consecutive students facing the same direction results in exactly 4 students facing South.

Therefore, a total of 4 students face the south direction.

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