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CA Foundation · Quantitative Aptitude · Ratio and Proportion, Indices and Logarithms

A variable Y is inversely proportional to the square of variable X. When X = 2, Y = 18. What will be the value of Y when X = 3?

Using inverse proportion Y = k/X², we find k = 72 from the given values. When X = 3, Y = 72/9 = 8. Inverse square relationships mean doubling X reduces Y by a factor of 4.

  1. A8Correct
  2. B10
  3. C12
  4. D16

Explanation

For inverse proportion: Y = k/X², where k is a constant. Using X = 2, Y = 18: 18 = k/4, so k = 72. When X = 3, Y = 72/9 = 8. A common mistake is treating it as direct proportion (Y = kX²), which would give Y = 2 × 9 = 18, or computing Y = 18 × (2/3)² = 18 × 4/9 = 8, arriving at the correct answer but with wrong reasoning.

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