Mean, median and series problem

[talkwithpreetham]

When five (not necessarily distinct) integers are put in ascending order, the median is 16 and the average of the smallest and largest integers is 15. Furthermore, when the smallest and largest numbers are removed from the set, the average of the new smallest and largest integers is 14. What is the smallest value that the largest of the original five integers could have?

This is a question from Manhatten practice tests.
According to them answer is 18.
Why can answer be 16 and series is ( 14,12,16,16,16)

[tommywallach]

Hey Preetham,

Do you mean "Why CAN'T the answer be xxx" or "Why CAN the answer be xxx"? Be really careful when writing stuff, because it makes it hard to answer.

Your example has not been put in ascending order.

-t