Operations on Rational Numbers

Let \(T = \{ a_1, a_2, ... , a_{30} \}\) and \(a_1 = n_1 + h_1, ... , a_{30} = n_{30} + h_{30}\) where \(n_i\)'s are integers and \(0 < h_i < 1\) for \(i \in \{1,...,30\}\).
Assume that \(a_1, ... , a_{10}\) have even tenths digits and \(a_{11}, ... , a_{30}\) have odd tenths digits.

Then we have followings.
\(S = a_1 + ... + a_{30} = n_1 + ... + n_{30} + h_1 + ... + h_{30}\).
\(E = ( n_1 - 1 ) + ... + ( n_{10} - 1 ) + ( n_{11} + 1 ) + ... + ( n_{30} - 1 ) = n_1 + ... + n_{30} - 10\).
\(E - S = n_1 + ... + n_{30} - 10 - ( n_1 + ... + n_30 ) - ( h_1 + ... + h_{30} ) = -10 - ( h_1 + ... + h_{30} )\)

Since \(0 < h_i < 1\) for all \(i \in \{ 1, ... , 30 \}\), we have \(0 < h_1 + ... + h_{30} < 30\).
Thus \(-40 < -10 - (h_1 + ... + h_{30}) < -10\).

There among the statements, only I is an answer.

Therefore, the correct choice is A.