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GATE 2018 CS – Question 7

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

If $pqr\ne0$ and $p^{-x}=\frac1q$, $q^{-y}=\frac1r$, $r^{-z}=\frac1p$, what is the value of the product $xyz$?

  1. $-1$
  2. $\frac1{pqr}$
  3. 1
  4. $pqr$

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Correct answer: (C) 1

Explanation

$p^x=q$, $q^y=r$ and $r^z=p$. So $p^{xyz}=(q)^{yz}=r^z=p$, which gives $xyz=1$.