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GATE 2018 CE (CE2) – Question 9

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

Given $\frac{\log P}{y-z}=\frac{\log Q}{z-x}=\frac{\log R}{x-y}=10$ for distinct x, y, z, find PQR.

  1. 0
  2. 1
  3. $xyz$
  4. $10xyz$

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Correct answer: (B) 1

Explanation

The ratios give $\log P=10(y-z)$, $\log Q=10(z-x)$ and $\log R=10(x-y)$. Adding cancels all variables: $\log(PQR)=0$. Thus PQR = 1 (B).