2010 AMC 10A Problem 4

Question

A book that is to be recorded onto compact discs takes

412

minutes to read aloud. Each disc can hold up to

56

minutes of reading. Assume that the smallest possible number of discs is used and that each disc contains the same length of reading. How many minutes of reading will each disc contain?

50.2

51.5

52.4

53.8

55.2

Answer: B

Concepts:divisibility estimation

Difficulty rating: 1030

Small hint:

Determine the minimum number of discs before averaging

Big hint:

7

discs hold too little, while

8

discs suffice

Solution:

Note that

7 \cdot 56 = 392

and

8 \cdot 56 = 448,

which means that the minimum number of discs needed is

8.

Then the minutes of reading that each disc contains is

412 \div 8 = 51.5.

Thus, B is the correct answer.