Question

Seven persons A, B, C, D, E, F and G are sitting in a straight line (not necessarily in the same order) facing North. Only two persons sit between F and G and G sits second to the left of B. D sits third to the left of C. E sits exactly between G and B and B sits at the extreme right end of row. Which of the following statements are correct?
(A) 'F' sits at the extreme left of the line.
(B) Two persons sit between 'E' and 'F'.
(C) 'C' sits exactly in the middle of the line.
(D) 'E' sits third to the right of 'A'.

• A. (A), (B) and (C) only
• B. (B), (C) and (D) only
• C. (C) and (D) only
• D. (A) and (C) only

Hint:

Start with fixed positions (like "extreme right end") to build the arrangement. Once the fixed points are established, relative clues (like "second to the left") become much easier to place.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a linear seating arrangement problem. We use the given clues to fix the positions of individuals relative to each other on a line.
Step 2: Detailed Explanation:
1. There are 7 positions, numbered 1 to 7 from left to right.
2. B sits at the extreme right end of the row: B is at position 7.
3. G sits second to the left of B: G is at position $7 - 2 = 5$.
4. E sits exactly between G and B: Since G is at 5 and B is at 7, E is at position 6.
5. Only two persons sit between F and G: G is at 5. Two persons to the left of G (positions 4 and 3) means F must be at position 2.
6. D sits third to the left of C: Possible pairs for (D, C) are (1, 4), (2, 5), (3, 6), etc. Since 5 and 6 are occupied, and 2 is occupied by F, the only available pair is D at 1 and C at 4.
7. Remaining person: Only position 3 is vacant, so A must be at position 3.
Final Arrangement: D(1), F(2), A(3), C(4), G(5), E(6), B(7).
Evaluating Statements:
(A) 'F' sits at the extreme left: No, D sits at the extreme left. (Incorrect)
(B) Two persons sit between 'E' and 'F': E is at 6, F is at 2. Between them are 3, 4, 5 (three persons). (Incorrect)
(C) 'C' sits exactly in the middle of the line: Position 4 is the middle of 7. (Correct)
(D) 'E' sits third to the right of 'A': A is at 3. Third right is $3 + 3 = 6$. E is at 6. (Correct)
Only (C) and (D) are correct.
Step 3: Final Answer:
The correct statements are (C) and (D) only, corresponding to option (3).