19. A list of positive integers has a median of 8 , a mode of 9 and a mean of 10 . What is the smallest possible number of integers in the list?
A 5
B 6
C 7
D 8
E 9
19. B From the information given, there are at least two 9 s in the list, since 9 is the mode, and at least one number greater than 10 , since 10 is the mean. So there are at least three numbers greater than 8 in the list. Therefore the list must contain at least six numbers, as the median of the numbers is 8 . Moreover, it is possible to find suitable lists of six numbers with sum 60 (as the mean is 10 ), for example 1 , $2,7,9,9,32$.