Which of the following statement is true and how?

Question

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 $Y$; $X$ is proportional to $Z$
2. For fixed $Z$; $X$ is proportional to $Y$
3. $XY/ Z$ is constant
4. For fixed $X$ ; $Z$ is proportional to $Y$.

My attempt: We see that $XY=\lambda Z\implies XY/Z=\lambda=\text{constant}$. Is it correct?

Answer 1

Number 2 is wrong. If we fix $Z$ we have

$$ XY = C $$

So $X$ isn't directly proportional to $Y$, as in $ X = YC $.

Also: your attempt is correct.