2011 AMC 12A Problem 3

Attempt Problem 3 of the 2011 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

A small bottle of shampoo can hold

35

milliliters of shampoo, whereas a large bottle can hold

500

milliliters of shampoo. Jasmine wants to buy the minimum number of small bottles necessary to completely fill a large bottle. How many bottles must she buy?

11

12

13

14

15

Answer: E

Concepts:floor and ceiling functions estimation

Difficulty rating: 880

Small hint:

Divide

500

35

Big hint:

Since

14

bottles fall short of

500,

round the quotient up

Solution:

Fourteen bottles hold

14 \cdot 35 = 490

milliliters, which is not enough. Fifteen bottles hold

15 \cdot 35 = 525

milliliters, which suffices.

So Jasmine needs

15

bottles.

Thus, the correct answer is E.