Problem 3 · Maximum and minimum of a quotient
A fraction grows with its numerator and shrinks with its denominator.
Integer answer, at most 4 digitsIf $x$ can vary between 5 and 10, and $y$ can vary between 20 and 80, what are the maximum and minimum values of $y/x$? (Concatenate the maximum and the minimum as your answer. For example, if the maximum were 56 and the minimum 2, you would answer 562.)
Copa Cangur · SCM
Easy
Closed answer
Reasoned solution
Key idea: to make a quotient large: big numerator, small denominator. To make it small: the other way round.
$$\max \frac{y}{x} = \frac{80}{5} = 16, \qquad \min \frac{y}{x} = \frac{20}{10} = 2.$$
Concatenating maximum and minimum: $16$ and $2$.
Answer: 162