Track / Stage 3 / 108 of 260 #108 of 1964

Problem 108

AMC 10/12, early questions

Number theory Difficulty 3.4 Multiple choice

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?

Pick one

Official solution

As all five options are divisible by $5$ , we may not use any pennies. (This is because a penny is the only coin that is not divisible by $5$ , and if we used between $1$ and $4$ pennies, the sum would not be divisible by $5$ .)
Hence the smallest coin we can use is a nickel, and thus the smallest amount we can get is $4\cdot 5 = 20$ . Therefore the option that is not reachable is $\boxed{15}$ $\Rightarrow$ $(A)$ .
We can verify that we can indeed get the other ones:

$25 = 10+5+5+5$
$35 = 10+10+10+5$
$45 = 25+10+5+5$
$55 = 25+10+10+10$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.