Percentage increase/decrease in two numbers to be multiplied

Question

$A \times B = C $

How do you determine if percentage increase in $A$ and an equivalent decrease percentage decrease in $B$ will result in the same number, bigger or lower numbers.

Many thanks

Answer 1

Hint: Think about the fact that $$\Big((1+r)A\Big)\cdot\Big((1-r)B\Big) = (1-r^2)\cdot AB$$

This will be less than/greater than/equal to $AB$ precisely when $1-r^2$ is less than/greater than/equal to $1$.

Consider these cases separately to see what must be true of $r$ in each case.