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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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sat Sep 04, 2021 5:58 pm

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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

OA D

Source: Magoosh

Source: Beat The GMAT — Problem Solving | Sat Sep 04, 2021 5:58 pm

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 8, the

by swerve » Tue Sep 07, 2021 3:14 am

BTGmoderatorDC wrote: ↑
Sat Sep 04, 2021 5:58 pm
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

From the question stem, we can get two equations:

\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

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