21. Each number in the sequence starting $2,3,6,8,8,4, \ldots$ is obtained in the following way. The first two numbers are 2 and 3 and afterwards each number is the last digit of the product of the two preceding numbers in the sequence. What is the 2017th number in the sequence?
A 8
B 6
C 4
D 3
E 2
21. E Continue the sequence as described to obtain $2,3,6,8,8,4,2,8,6,8,8,4,2,8,6,8$ and so on. Since the value of each term depends only on the preceding two terms, it can be seen that, after the first two terms, the sequence $6,8,8,4,2,8$ repeats for ever. Now $2017-2=335 \times 6+5$. Therefore the 2017th number in the sequence is the fifth number of the repeating sequence $6,8,8,4,2,8$. Hence the required number is 2 .