Problem 10 · Extremal reasoning with reordered increases · 4 points
Made by AI and not reviewed by a real person.
Imagine the four monthly savings increases happened in a different order, while January’s savings stayed the same. Which month’s plotted total could never be made lower by reordering the increases, but could be made higher?
- April
- February
- May
- March
- January
Show a hint
- Reordering the increases changes which ones have happened by a given month, but not the final total. Think about what would make an intermediate total as small as possible.
- The four increases are $15, $10, $30, and $15. For each month, consider which increases would have to happen first to give the smallest possible total.
Show the answer and solution
Answer: D — March
By March, the chart has used the $15 and $10 increases—the two smallest—so no reordering can lower March’s total. Putting the $30 increase before March could make it higher. February’s total could be lowered by putting $10 first, and April’s could be lowered by saving the $30 increase for last. January and May are tempting because their totals cannot be lowered, but reordering cannot make either one higher.