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1 vote

An engineer measures THREE quantities, $X, Y$ and $Z$ in an experiment. She finds that they follow a relationship that is represented in the figure below$: ($the product of $X$ and $Y$ linearly varies with $Z)$

Then, which of the following statements is FALSE?

  1. For fixed $Z$; $X$ is proportional to $Y$
  2. For fixed $Y$; $X$ is proportional to $Z$
  3. For fixed $X$; $Z$ is proportional to $Y$
  4. $XY/Z$ is constant
in Numerical Ability 4.9k points
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1 Answer

1 vote
 
Best answer

Given that, $XY \propto Z \implies XY = k Z;$ where $k$ is constant.

Now, we can verify each and every option.

  1. For fixed $Z; X$ is proportional to $Y{\color{Red} {\text{ – False.}}}$
    • $XY \propto Z$
    • For fixed $Z,$ we can write $XY \propto 1$
    • $X \propto \dfrac{1}{Y}\;\text{(or)} \; Y \propto \dfrac{1}{X}$
  2. For fixed $Y; X$ is proportional to $Z-$ True.
    • $XY \propto Z$
    • For fixed $Y,$ we can write $X \propto Z$
  3. For fixed $X; Z$ is proportional to $Y-$ True.
    • $XY \propto Z$
    • For fixed $X$ we can write $Y \propto Z$
  4. $XY/Z$ is constant –  True.
    • $XY \propto Z$
    • $\implies XY = k Z;$ where $k$ is constant. 

So, the correct answer is A.

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