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
OA D
Source: Magoosh
When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the
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From the question stem, we can get two equations:BTGmoderatorDC wrote: ↑Sat Sep 04, 2021 5:58 pmWhen 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
OA D
Source: Magoosh
\begin{align*}
\begin{cases}
x=11y+4 &\quad (1) \\
2x=8(3y)+2 &\quad (2)
\end{cases}
\end{align*}
Now, subtracting \((2)\) from \((1),\) we get:
\(x = 13y + 2 \Rightarrow 13y  x = 2 \Rightarrow \) D