Step-by-step Solution:

Solution Breakdown

Let's deduce the seating arrangement and the directions everyone is facing by analyzing the given clues step-by-step.

Step 1: Understand the Seating and Facing Directions

The four people are seated at the North, East, South, and West sides of a table, facing the center. This means:

• The person at the North seat is facing South.
• The person at the East seat is facing West.
• The person at the South seat is facing North.
• The person at the West seat is facing East.

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Step 2: Apply the Clues to Determine Positions

1. Clue: "One girl is facing South."
   Based on our setup, to face South, a person must be sitting in the North seat. So, we place a girl at the North position.
2. Clue: "Persons sitting opposite to each other are not of the same sex."
   The seat opposite North is South. Since a girl is in the North seat, a boy must be in the South seat.
3. Clue: "No boy is facing East."
   To face East, a person must be in the West seat. This clue tells us a boy cannot be in the West seat. Since the only remaining seats are West and East, and we have one boy and one girl left to place, the remaining girl must take the West seat.
4. Final Placement: By elimination, the second boy must be in the last available seat, which is the East position.

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Step 3: Identify the Directions the Boys are Facing

Now we find the directions the two boys are facing based on their final positions:

• The boy in the South seat is facing North.
• The boy in the East seat is facing West.

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Conclusion

The directions the two boys are facing are North and West.

This corresponds to option A.