Mathematical Thinking | HUMAT

Can somebody explain me how do solve this question?

p.s. Are you also taking the HUMAT? I’m also taking it, where did you find the past papers? I’ve been searching past papers but there aren’t many. Could you please share it with me also? My mail is guybone1010@gmail.com. Thank you so much!

In the first graph: X is constant and Y ∝ Z^2.
This implies that Y = cZ^2 for some constant c.
Substituting Y ∝ Z^2 into the equation X^a * Y^b = kZ^-2 , we get b = -1.

In the second graph: Y is constant and Z ∝ X.
This implies that Z = cX for some constant c.
Substituting Z ∝ X into the equation, we get a = -2.

To check lets look at third graph where Z is constant and Y ∝ X^-1.
This implies Y = cX^-1 for some constant c, which fits with a = -2 and b = -1.

So final answer: a = -2 and b = -1 which is D.