csat-suneung 2011 Q28

csat-suneung · South-Korea · csat__math-humanities 4 marks Matrices Linear System and Inverse Existence
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 TakerABC
$p$455045
$q$405050

(1) $a > b > c$
(2) $a > c > b$
(3) $b > a > c$
(4) $b > c > a$
(5) $c > b > a$
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]
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
Converted Score / Test Taker & A & B & C \\
\hline
$p$ & 45 & 50 & 45 \\
\hline
$q$ & 40 & 50 & 50 \\
\hline
\end{tabular}
\end{center}
(1) $a > b > c$\\
(2) $a > c > b$\\
(3) $b > a > c$\\
(4) $b > c > a$\\
(5) $c > b > a$