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A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 1/4. Three stones A, B and C are placed at the points (1,1), (2,2) and (4,4) respectively. Then which of these stones is / are on the path of the man? (1) A only (2) C only (3) All the three (4) B only

1. A only
2. C only
3. All the three
4. B only

Correct answer: B only

Solution

The arithmetic mean of the reciprocals of the intercepts indicates that the line has a specific slope, which can be calculated from the given mean. The line's equation derived from the intercepts shows that it passes through point C (4,4) but does not pass through points A (1,1) or B (2,2), making C the only stone on the man's path.

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