Problem 15 · 2017 Math Kangaroo
Medium
Logic & Word Problems
work-backward
Boris wants to increase his pocket money. A fairy gives him three magic wands, and he must use every one exactly once: the “+1” wand increases his money by 1 €, the “−1” wand decreases it by 1 €, and the “×2” wand doubles it. In which order should he use the wands to end up with the most money?
Show answer
Answer: D
Show hints
Hint 1 of 2
Doubling multiplies everything that came before, so a +1 done before doubling is worth more than after.
Still stuck? Show hint 2 →
Hint 2 of 2
Add before you double and subtract after you double to end up highest.
Show solution
Approach: order operations so the gain is doubled and the loss is not
- The +1 wand is most valuable applied before the ×2 wand, so its euro gets doubled.
- The −1 wand should come after the ×2 wand, so only one euro is lost, not two.
- Best order: +1, then ×2, then −1, giving (x+1)×2 − 1 = 2x + 1.
- The picture showing that order is (D).
Mark:
· log in to save