Problem 12 · Exchange argument · 4 points
Made by AI and not reviewed by a real person.
Four sticker printers make 1, 2, 3, or 4 stickers per minute, and four batteries last 2, 5, 9, or 14 minutes each, regardless of printer. If each printer gets one battery and runs it empty, what is the second-largest total number of stickers possible?
- 95
- 90
- 94
- 92
- 91
Show a hint
- What happens if a faster printer gets a shorter-lasting battery than a slower printer?
- Start with the best assignment, then look for the smallest loss from a swap.
Show the answer and solution
Answer: D — 92
If a faster printer has a shorter-lasting battery than a slower printer, swapping their batteries increases the total. So the largest total pairs the printers and batteries in increasing order: 1×2 + 2×5 + 3×9 + 4×14 = 95. In any other assignment, such a swap can increase the total by at least (2−1)(5−2) = 3, so no other total exceeds 92. Swapping the 2- and 5-minute batteries in the best assignment loses exactly 3, giving 92. The tempting choice 95 is the largest total, not the second-largest.