Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least. Whenever F scores the highest, B scores the least. In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A. If E is ranked third, then which one of the following is correct?

The problem provides several conditions about the ranks of six students (A, B, C, D, E, F) in a test. We need to determine the correct statement if E is ranked third. Let's break down the given information: 1. **Highest Scorer:** Either C or F scores the highest. 2. **Conditional Least Scorer:** * If C scores highest, then E scores the least (6th rank). * If F scores highest, then B scores the least (6th rank). 3. **Relative Ranks:** * D scores higher than A (D > A). * A scores higher than B (A > B). * C scores higher than A (C > A). * "D scores higher than A, but they are close competitors" implies D and A are adjacent in rank, with D immediately above A. Now, let's apply the condition "If E is ranked third": Step 1: Determine the highest and lowest scorers. * If C were highest (1st rank), then E would be least (6th rank). This contradicts the given information that E is ranked third. * Therefore, C cannot be highest. F must be the highest scorer (1st rank). * Since F scores highest, according to condition 2, B scores the least (6th rank). So far, we have: 1st: F 2nd: ? 3rd: E (given) 4th: ? 5th: ? 6th: B Step 2: Place A and D using the "close competitors" condition. * We know D > A, and they are adjacent. This means D is immediately above A in rank. * From the relative ranks, we have C > A > B. Since B is 6th, A must be higher than 6th. * A cannot be 1st (F is 1st), 3rd (E is 3rd), or 6th (B is 6th). So A can be 2nd, 4th, or 5th. * If A is 2nd, then D would have to be 1st (to be immediately above A), but F is 1st. So A cannot be 2nd. * If A is 4th, then D would have to be 3rd (to be immediately above A), but E is 3rd. So A cannot be 4th. * Therefore, A must be 5th. * If A is 5th, then D must be 4th (to be immediately above A). Now the ranking looks like this: 1st: F 2nd: ? 3rd: E 4th: D 5th: A 6th: B Step 3: Place the remaining student (C). * The only remaining student is C, and the only remaining rank is 2nd. * So, C must be 2nd. The complete and unique ranking is: F (1st) > C (2nd) > E (3rd) > D (4th) > A (5th) > B (6th). Step 4: Evaluate the options based on this ranking. A) E gets more marks than C. E is 3rd, C is 2nd. C gets more marks than E. So, this statement is False. B) C gets more marks than E. C is 2nd, E is 3rd. C gets more marks than E. So, this statement is True. C) A is ranked fourth. A is ranked fifth. So, this statement is False. D) D is ranked fifth. D is ranked fourth. So, this statement is False. Therefore, the correct statement is B. The final answer is B