2011 AMC 10A Problem 2

Question

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:divisibility estimation

Difficulty rating: 660

Small hint:

Compare multiples of

35

to

500

Big hint:

The first multiple of

35

that reaches

500

gives the number of bottles

Solution:

The desired amount is

\dfrac{500}{35} = \dfrac{100}{7} = 14 \dfrac{2}{7}.

This means that the smallest number of small bottles she must buy is

15.

Thus, E is the correct answer.