Problem Solving

List \(T\) consists of \(30\) positive decimals, none of which is an integer, and the sum of the \(30\) decimals is \(S.\) The estimated sum of the \(30\) decimals, \(E,\) is defined as follows. Each decimal in \(T\) whose tenths digit is even is rounded up to the nearest integer, and each decimal in \(T\) whose tenths digits is odd is rounded down to the nearest integer. If \(\dfrac13\) of the decimals in \(T\) have a tenths digit that is even, which of the following is a possible value of \(E - S ?\)

I. \(-16\)
II. \(6\)
III. \(10\)

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Answer: B

Source: Official Guide