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GATE 2016 ME (ME1) – Question 9

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

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

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

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Show answer and explanation

Correct answer: (C) 1

Explanation

For positive non-unit bases, take logarithms of q^(−a)=1/r to obtain a ln q=ln r. Similarly b ln r=ln s and c ln s=ln q. Multiplying and cancelling nonzero logarithms gives **abc=1, C**. If q=r=s=1 the exponents are unconstrained, so the usual non-unit-base assumption is required.