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CAT 2023 Set-1 | Quantitative Aptitude | Question: 21

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For some positive and distinct real numbers $x, y$ and $z$, if $\frac{1}{\sqrt{y}+\sqrt{z}}$ is the arithmetic mean of $\frac{1}{\sqrt{x}+\sqrt{z}}$ and $\frac{1}{\sqrt{x}+\sqrt{y}}$, then the relationship which will always hold true, is

  1. $y, x$ and $z$ are in arithmetic progression
  2. $\sqrt{x}, \sqrt{y}$ and $\sqrt{z}$ are in arithmetic progression
  3. $x, y$ and $z$ are in arithmetic progression
  4. $\sqrt{x}, \sqrt{z}$ and $\sqrt{y}$ are in arithmetic progression
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