Which of the following pairs $(x, y)$ are NOT in direct proportion?

Which of the following pairs $(x, y)$ are NOT in direct proportion?
  1. $(2, 6), (4, 12), (5, 15)$
  2. $(1, 5), (2, 10), (3, 15)$
  3. $(3, 9), (4, 12), (6, 20)$
  4. $(1, 7), (2, 14), (3, 21)$

Solution

Check $\dfrac{x}{y}$. In (c): $\dfrac{3}{9} = \dfrac{1}{3}$, $\dfrac{4}{12} = \dfrac{1}{3}$, but $\dfrac{6}{20} = \dfrac{3}{10}$. Not constant, so not direct.

Asked in: IMO

Practice more DIRECT AND INVERSE PROPORTIONS questions on Aicharya