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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. B only
3. All the three
4. D only

Correct answer: B only

Solution

Line x/a + y/b = 1 with mean of reciprocal intercepts (1/a+1/b)/2 = 1/4 gives 1/a+1/b = 1/2. A point (k,k) lies on it when k(1/a+1/b)=1 -> k(1/2)=1 -> k=2. So only (2,2), stone B, is on the path.

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