GAUSS8 2022 Problem 25

Student A, Student B, and Student C have been hired to help scientists develop a new flavour of juice. There are 4200 samples to test. Each sample either contains blueberry or does not. Each student is asked to taste each sample and report whether or not they think it contains blueberry. Student A reports correctly on exactly 90 \% of the samples containing blueberry and reports correctly on exactly 88 \% of the samples that do not contain blueberry. The results for all three students are shown below.

\begin{array}{|c|c|c|c|} \hline & \text { Student A } & \text { Student B } & \text { Student C } \\ \hline \begin{array}{c} \text { Percentage correct on samples } \\ \text { containing blueberry } \end{array} & 90 \% & 98 \% & (2 m) \% \\ \hline \begin{array}{c} \text { Percentage correct on samples } \\ \text { not containing blueberry } \end{array} & 88 \% & 86 \% & (4 m) \% \\ \hline \end{array}

Student B reports 315 more samples as containing blueberry than Student A. For some positive integers m, the total number of samples that the three students report as containing blueberry is equal to a multiple of 5 between 8000 and 9000. The sum of all such values of m is

Answer Choices
A. 45
B. 36
C. 24
D. 27
E. 29