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

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

by Vincen » Mon Feb 15, 2021 7:51 am

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

by swerve » Mon Feb 15, 2021 4:11 pm
Vincen wrote: ↑
Mon Feb 15, 2021 7:51 am
 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
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