When positive integer \(x\) is divided by \(11,\) the quotient is \(y\) and the remainder is \(4.\) When \(2x\) is divid

[Vincen]

When positive integer \(x\) is divided by \(11,\) the quotient is \(y\) and the remainder is \(4.\) When \(2x\) is divided by \(8,\) the quotient is \(3y\) and the remainder is \(2.\) What is the value of \(13y - x ?\)

A. -4
B. -2
C. 0
D. 2
E. 4

Answer: D

Source: Magoosh

[swerve]

When positive integer \(x\) is divided by \(11,\) the quotient is \(y\) and the remainder is \(4.\) When \(2x\) is divided by \(8,\) the quotient is \(3y\) and the remainder is \(2.\) What is the value of \(13y - x ?\)

A. -4
B. -2
C. 0
D. 2
E. 4

Answer: D

Source: Magoosh

From the question stem, we can get two equations as below:
\begin{align*}
\begin{cases}
x=11y+4 \\
\quad &\Longrightarrow \quad
11y+4=12y+1
\quad \Longrightarrow \quad
y=3, \quad x=37\\
x=12y+1
\end{cases}
\end{align*}

So, \(13y-x = 13(3)-37 \Longrightarrow 2\)

Therefore, D