Question Details

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.


Question: If F stands second in the ranking, then the position of B is

Options

A

Third

B

Fourth

C

Fifth

D

Sixth

Show Answer

Correct Answer :

Option C

Fifth

Solution :

The correct option is Fifth.

Let us analyze the given conditions step-by-step to determine the ranking of the six students: A, B, C, D, E, and F.
The ranking goes from 1st (highest score) to 6th (least score).

1. Analyze the rules for the highest and least scorers:
- Either C or F scores the highest (1st position).
- Rule 1: If C is 1st, then E is 6th (scores the least).
- Rule 2: If F is 1st, then B is 6th (scores the least).

2. Analyze the relative rankings given in the problem:
- D scores higher than A, and they are close competitors (meaning no one scores between D and A, so they are adjacent: D immediately followed by A, represented as DA).
- A scores higher than B (D > A > B).
- C scores higher than A (C > A).

3. Use the specific condition for this question:
We are given that F stands second (2nd) in the ranking.
Since F is 2nd, F cannot be 1st. Therefore, the highest scorer (1st position) must be C.
According to Rule 1, since C scores the highest (1st), E must score the least (6th).

4. Construct the ranking positions:
Let the positions from 1st to 6th be represented as:
1st: C
2nd: F
3rd: _
4th: _
5th: _
6th: E

We have three remaining students to place in the 3rd, 4th, and 5th positions: D, A, and B.
We know from the relative rankings that:
- D and A are close competitors, meaning they must occupy adjacent positions with D ahead of A (DA).
- A scores higher than B, so B must be ranked lower than A.

Thus, the order of the remaining three students must be D, then A, then B.
Placing them in the available spots (3rd, 4th, and 5th) gives:
3rd: D
4th: A
5th: B

Therefore, the complete ranking list from 1st to 6th is:
1. C
2. F
3. D
4. A
5. B
6. E

Thus, the position of B in the ranking is Fifth.

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