Which of the following pairs $(x, y)$ are in inverse proportion?

Which of the following pairs $(x, y)$ are in inverse proportion?
  1. $(2, 18), (3, 12), (4, 9)$
  2. $(2, 4), (3, 6), (4, 8)$
  3. $(1, 2), (2, 4), (3, 8)$
  4. $(2, 5), (4, 10), (6, 15)$

Solution

In (a): $2 \times 18 = 36$, $3 \times 12 = 36$, $4 \times 9 = 36$. All equal, so inverse.

Asked in: IMO

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