Question

Directions: A circular field, with inner radius of 10 meters and outer radius of 20 meters, was divided into five successive stages for ploughing. The ploughing of each stage was handed over to a different farmer.

1. Farmers are referred to by the symbols F1, F2, F3, F4, F5.
2. The points between different stages are referred to by the symbols P1, P2, P3, P4, P5, not necessarily in that order.
3. Farmer F5 was given the work of ploughing the stage starting at point P4.
4. The stage from point P5 to point P3 was not the first stage.
5. Farmer F4 was given the work of the fourth stage.
6. Stage 3 finished at point P1, and the work of which was not given to farmer F1.
7. Farmer F3 was given the work of the stage ending at point P5.

Which were the starting and finishing points for stage 2?

• A. P2 and P5
• B. P5 and P3
• C. P3 and P1
• D. P5 and P4

Hint:

Fix stage 3's finish point first using clue 6, then use clue 4 to place the P5-to-P3 stage, and use clues 3 and 7 to resolve the last two points.

Answer 1

The Correct Option is B

Instead of building the full loop first, test each option against the seven clues and see which one survives, since only one arrangement of points and farmers can satisfy all seven conditions at once.

1. P2 and P5: If stage 2 ran from P2 to P5, then combined with clue 6 (stage 3 finishes at P1), stage 3 would have to start at P5. Working the rest of the loop out from there, clue 3 (F5 starts at P4) and clue 7 (F3 ends at P5) end up pointing at the same stage, which cannot happen. This option fails.
2. P5 and P3: Placing "P5 to P3" as stage 2 leaves P1 as stage 3's finish, matching clue 6 directly, and lets P2 and P4 slot into stage 1 and stage 5 without any clash. Every one of clues 3, 5, and 7 holds in this layout. This option survives.
3. P3 and P1: This would make stage 2 finish at P1, but clue 6 already fixes P1 as the finish of stage 3. Two different stages cannot finish at the same point in a five-stage loop, so this is impossible.
4. P5 and P4: This forces stage 3, which must finish at P1 by clue 6, to start right after P4, leaving no consistent place for the "P5 to P3" stage required by clue 4. This option fails too.

Only "P5 and P3" keeps all seven clues true at once, so stage 2 starts at P5 and finishes at P3.

Let's summarize:

• The five stages form a loop, so each stage's finish point is the next stage's start point.
• Clue 6 anchors stage 3's finish at P1, the fastest peg to start from.
• Testing each option against that peg and the rest of the clues quickly rules out three of the four choices.

The correct answer is that stage 2 goes from P5 to P3.