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Cars emerging from a motorway arrive at a junction that

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Cars emerging from a motorway arrive at a junction that

by AAPL » Thu Nov 07, 2019 12:11 pm
Economist GMAT

Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 700 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 700 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?

A. 1300
B. 1500
C. 1700
D. 1900
E. 2100

OA C
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by deloitte247 » Sat Nov 09, 2019 2:05 pm
If 700 cars per hour were diverted from the left lane to the right lane, then the right lane will be twice of the left lane.
Right lane + 700 = 2 (left lane - 700)
If 700 cars were diverted from the right lane to the left, then the left lane would be 4 times as great as the number of cars entering the right lane per hour.
Left lane + 700 = 4 (right lane - 700)
Let the right lane = r
Let the left lane = l
r + 700 = 2 (l-700) --- eqn. (i)
l + 700 = 4 (r-700) --- eqn. (ii)
So, how many cars enter the left lane per hour?
From eqn. (i); r + 700 = 2 (l-700)
r + 700 = 2l - 1400
r = 2l - 2100
From eqn. (ii)
l + 700 = 4 (r-700)
where r = 2l - 2100
l + 700 = 4(2l - 2100-700)
l + 700 = 4(2l - 2800)
l + 700 = 8l - 11200
-7l = -11900
Divide both sides by -7
$$l=\frac{-11900}{-7}=1700$$
Therefore, 1700 cars entered the left lane per hour. Hence, the correct answer is option C
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Cars emerging from a motorway arrive at a junction that

by swerve » Sun Nov 10, 2019 10:06 am
AAPL wrote:Economist GMAT

Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 700 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 700 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?

A. 1300
B. 1500
C. 1700
D. 1900
E. 2100

OA C
Here we have

\begin{align*}
\begin{cases}
R+700 &=2(L-700)\\
L+700 &=4(R-700)
\end{cases}
\quad \Rightarrow \quad
L=1700
\end{align*}
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