A certain company converts the raw scores of applicants' reasoning ability test and spatial perception ability test for use. When the raw score of the reasoning ability test is $x$ and the raw score of the spatial perception ability test is $y$, the two converted scores $p$ and $q$ are as follows. $$\binom { p } { q } = \left( \begin{array} { l l } 3 & 2 \\ 2 & 3 \end{array} \right) \binom { x } { y }$$ When the converted scores of applicants A, B, and C are as shown in the table, let the raw scores of applicants A, B, and C on the reasoning ability test be $a , b , c$, respectively. Which of the following correctly represents the order of magnitude of $a , b , c$? [4 points]
| Converted Score / Test Taker | A | B | C |
| $p$ | 45 | 50 | 45 |
| $q$ | 40 | 50 | 50 |
(1) $a > b > c$
(2) $a > c > b$
(3) $b > a > c$
(4) $b > c > a$
(5) $c > b > a$