Question

This group of questions is based on a set of conditions. In answering some of the questions, it may help to draw a rough diagram. Choose the response that most accurately and completely answers each question.

A circular field, with an inner radius of 10 meters and an 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 following symbols: F1, F2, F3, F4, F5.
2. The points between different stages of the project are referred to by the following 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 it was not given to farmer F1.
7. Farmer F3 was given the work of the stage ending at point P5.

Which was the finish point for farmer F2?

• A. P1
• B. P2
• C. P3
• D. P4

Hint:

Chain the stages forward from the fixed Stage 3 to P1 clue and the F3 ends-at-P5 clue, which pins Stage 1 to F3 and Stage 3 (ending at P1) to F2, since condition 6 rules F1 out of Stage 3.

Answer 1

The Correct Option is A

Step 1: Build a stage-to-point table from the two most specific clues first.
Condition 6 (Stage 3 ends at P1) and condition 7 (F3's stage ends at P5) are the two most specific facts, so start there. If F3's stage were Stage 3, it would have to end at P1 (from condition 6) and at P5 (from condition 7) at the same time, which is impossible, so F3 is NOT doing Stage 3.

Step 2: Use condition 4 to pin down where F3's stage sits.
Condition 4 says the P5-to-P3 stage is not Stage 1. Since F3's stage ends at P5, the stage right after F3's must be the one running P5 to P3, and that following stage cannot be Stage 1 (condition 4). Checking the stages in order, if F3 has Stage 1, the next stage (Stage 2) would be the P5-to-P3 one, which condition 4 allows since Stage 2 is not Stage 1, so this fits: F3 does Stage 1, ending at P5, and Stage 2 runs P5 to P3.

Step 3: Extend the chain using condition 6 again.
Stage 3 starts where Stage 2 ends, at P3, and condition 6 already tells us Stage 3 ends at P1. So Stage 3 goes P3 to P1.

Step 4: Bring in F5 and F4 to finish the point-labelling.
Condition 3 puts F5's stage starting at P4; since Stage 1 is taken by F3, F5 must be doing Stage 5, so Stage 5 starts at P4. Condition 5 gives Stage 4 to F4, running from Stage 3's end (P1) to Stage 5's start (P4), so Stage 4 is P1 to P4. The one label left over, P2, must be where Stage 5 ends and Stage 1 begins.

Step 5: Finish assigning farmers and read off F2.
Stage 1 is F3's and Stage 4 is F4's; Stage 5 is F5's (Step 4). That leaves Stage 2 and Stage 3 for F1 and F2. Condition 6 says F1 was NOT given Stage 3, so F1 has Stage 2 and F2 has Stage 3, which runs from P3 to P1.

Final Answer:
F2's finish point was P1. \[ \boxed{P1} \]