14) The Orue is a currency that has only two coins, worth 3 and 11 cents. What is the largest amount that cannot be paid exactly?

$\begin{array}{llll}\text { (A) } 16 \text { cents } & \text { (B) } 19 \text { cents } & \text { (C) } 20 \text { cents } & \text { (D) } 32 \text { cents }\end{array}$

(E) there are arbitrarily large amounts that cannot be paid exactly.
14) The answer is (B). Clearly, 19 cents cannot be paid, because neither 19 nor 8 are multiples of 3. On the other hand, all multiples of 3 can be paid, all numbers of the form $3k+1$ that are greater than or equal to 22, and all numbers of the form $3k+2$ that are greater than or equal to 11. Therefore, 19 is precisely the maximum excluded number.