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GATE 2016 EC – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

If $q^{-a} = \frac{1}{r}$ and $r^{-b} = \frac{1}{s}$ and $s^{-c} = \frac{1}{q}$, the value of $abc$ is ____.

  1. $(rqs)^{-1}$
  2. 0
  3. 1
  4. $r + q + s$

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Correct answer: (C) 1

Explanation

The three equations give $q^a = r$, $r^b = s$ and $s^c = q$. Substituting step by step, $q = s^c = (r^b)^c = r^{bc} = (q^a)^{bc} = q^{abc}$. So $q^{abc} = q$, which means $abc = 1$.