Discussion
Suppose that x is directly proportional to y and inversely proportional to the square of z. If both y and z are increased by 50%, then the percentage change in x will be:
Answer: C
The change is 33.33% (a decrease).
Since x = k y / z2, raising y and z by 50% multiplies y by 1.5 and z2 by 2.25.
\[ \frac{1.5}{2.25}=\frac{2}{3} \]
So x becomes two-thirds of its old value, a fall of 33.33%. 15%, 30% and 35% do not match this factor.
When one quantity is directly proportional to y and inversely proportional to the square of z, the new value is found by multiplying the old value by the changes. A rise of 50% is a factor 1.5. Dividing by 1.5 squared, 2.25, and multiplying by 1.5 gives the factor 2/3.
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