Three variables x, y and z are known to be related to each other in the following ways:

• x is directly proportional to the square of z

• y is inversely proportional to the cube of z.

Which of the following correctly describes the relationship between x and y?

Answer:

16) D

Let us write down the information given into proportions first.

x ∝ z²
y ∝ ¹⁄z³

Making powers equal,

x³ ∝ z⁶       (eq 1)

y² ∝ ¹⁄z⁶
z⁶ ∝ ¹⁄y²       (eq 2)

Using eq 1 and 2,

z ∝ x³ ∝ ¹⁄y²

So the cube of x is inversely proportional to the square of y.