Problem 13 · 2018 Math Kangaroo
Medium
Arithmetic & Operations
divisionestimate-and-pick
Philipp wants to know how much his book weighs, correct to half a gram. However, his scale only shows weights correct to 10 g, so he weighs several identical books all together. What is the minimum number of identical books he has to put on the scale to reach his aim?
Show answer
Answer: D — 20
Show hints
Hint 1 of 3
Reading to the nearest 10 g means the true total is off by at most 5 g.
Still stuck? Show hint 2 →
Hint 2 of 3
To know one book to the nearest half-gram, the per-book error must be small enough to round correctly — under a quarter of a gram.
Still stuck? Show hint 3 →
Hint 3 of 3
Share that 5 g total error among n books and make 5/n small enough.
Show solution
Approach: bound the per-book error so it rounds to the nearest half-gram
- A reading correct to 10 g can be off by up to 5 g from the true total.
- Dividing by n books, one book's value is off by up to 5/n g; to pin it to the nearest half-gram the error must stay below 0.25 g, so 5/n ≤ 0.25.
- That needs n ≥ 20, so the minimum is 20 books.
Mark:
· log in to save