8) Near a water source, there is a cistern with a capacity greater than 30 hectoliters, initially empty. Only two calibrated containers, one of 15 liters and one of 21 liters, are available, with which it is possible to add and remove water from the cistern. Which of the following volumes of water cannot be placed exactly in the cistern?
(A) 3 liters
(B) 5 liters
$\begin{array}{lll}\text { (C) } 6 \text { liters } & \text { (D) } 645 \text { liters }\end{array}$
(E) I can obtain all of the above.
8) The answer is (B).

By adding and removing volumes of 21 and 15 liters, I can obtain all and only the volumes (positive or null) of the type $\pm m \cdot 21 \pm n \cdot 15$ with $m, n$ integers. Since 21 and 15 are divisible by 3, I obtain only volumes divisible by 3, so I cannot have 5 liters. Note that $3=3 \cdot 15-2 \cdot 21$ is an obtainable volume, and therefore all multiples of 3 are.