Understanding the Exam Marks Ranking

We are given six individuals (A, B, C, D, E, F) with distinct exam scores. We need to determine a possible score for A based on the provided clues.

Establishing the Score Order

Key information provided:

• B scored the third highest marks.
• The third highest score is 80 marks. Therefore, B's score is 80.
• F scored 94 marks. Since scores are distinct and F scored higher than A and D (F > A > D), F must have the highest score (1st).
• E scored more marks than only C. This implies C has the lowest score (6th) and E has the second lowest score (5th).

Based on this, the ranking order is:

1. F (94 marks)
2. 2nd highest
3. B (80 marks)
4. 4th highest
5. E
6. C (Lowest)

We know the relationship F > A > D. Since F is 1st (94) and B is 3rd (80), and E is 5th, C is 6th, the only remaining positions for A and D are 2nd and 4th.

To satisfy F > A > D:

• A must score more than D.
• A must score less than F (94).

If A were placed 4th, then D would have to be 5th or 6th. However, E is 5th and C is 6th. This placement is impossible for A and D as distinct individuals.

Therefore, A must be in the 2nd position. The order becomes: F > A > B > D > E > C.

This requires A's score to be between F's score (94) and B's score (80), because A is ranked 2nd and B is ranked 3rd.

The condition F > A > D is satisfied if 94 > A > 80 and D scores less than 80 (placed 4th).

So, A's score must satisfy the inequality:

$ 94 > \text{A's Score} > 80 $

Validating A's Score Option

Now, let's check the given options against the condition $ 94 > \text{A's Score} > 80 $:

• Option 1: 91. Does $ 94 > 91 > 80 $ hold true? Yes.
• Option 2: 60. Does $ 94 > 60 > 80 $ hold true? No.
• Option 3: 96. Does $ 94 > 96 > 80 $ hold true? No.
• Option 4: 75. Does $ 94 > 75 > 80 $ hold true? No.

Only the score 91 falls within the possible range for A.