16. Eight cards are numbered from 1 to 8 . The cards are placed in two boxes $P$ and $Q$ so that the sum of the numbers on the three cards in box $P$ is equal to the sum of the numbers on the five cards in box $Q$. Which of the following statements must be true?
A The card numbered 1 is not in box $Q$
B Four cards in box $Q$ have even numbers on
C The card numbered 5 is in box $Q$
D The card numbered 2 is in box $Q$
E Exactly three cards in box $Q$ have odd numbers on.
16. D Note first that the sum of the numbers on the eight cards is 36 . Therefore the sum of the numbers on the cards in each of the boxes is 18 . There are only three cards in box $P$ and hence the possible combinations for the numbers on the cards in box $P$ are $(8,7,3),(8,6,4)$ and $(7,6,5)$ with the corresponding combinations for box $Q$ being $(6,5,4,2,1),(7,5,3,2,1)$ and $(8,4,3,2,1)$. The only statement which is true for all three possible combinations for box $Q$ is that the card numbered 2 is in box $Q$. Hence the only statement which must be true is statement $\mathrm{D}$.