Question

In the United States, coins have the following thicknesses: penny, $1.55$ mm; nickel, $1.95$ mm; dime, $1.35$ mm; quarter, $1.75$ mm. If a stack of these coins is exactly $14$ mm high, how many coins are in the stack?

$7$

$8$

$9$

$10$

$11$

Solution:

Each thickness ends with $5$ in the hundredths place. A stack of an odd number of coins keeps a $5$ there, and pairs give an odd digit in the tenths place, so a whole-number height requires the count to be a multiple of $4.$

A stack of $4$ coins is at most $4(1.95) = 7.8$ mm, and a stack of $12$ coins is at least $12(1.35) = 16.2$ mm, so only $8$ coins can total $14$ mm.

Indeed, $8$ quarters give $8(1.75) = 14$ mm.

Thus, the correct answer is B.

2004 AMC 10B Problem 13

Solution:

Problem 13 in Other Years