2009 AMC 10A Problem 2

Question

Four coins are picked out of a piggy bank that contains a collection of pennies, nickels, dimes, and quarters. Which of the following could not be the total value of the four coins, in cents?

15

25

35

45

55

Answer: A

Concepts:money divisibility bounding to limit cases

Difficulty rating: 940

Small hint:

A total that is a multiple of

5

forces the number of pennies to be a multiple of

5

Big hint:

With no pennies, four coins are worth at least

4 \cdot 5 = 20

cents

Solution:

To get a multiple of

5

cents, the number of pennies must be a multiple of

5.

With only four coins, that means using no pennies, but then the four coins are each worth at least

5

cents, for a total of at least

20

cents.

So

15

cents cannot be made. The others can:

25 = 10 + 3(5),

35 = 3(10) + 5,

45 = 25 + 10 + 2(5),

and

55 = 25 + 3(10).

Thus, the correct answer is A.