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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

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Source: 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

The OA is C

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Let represent the right lane with 'x' and the left lane with 'y'. No of cars per hour is constant.
For right lane,
$$x+700=2\left(y-700\right)\ \ \ \ \ \ -----\ eqn\ i$$
For left lane,
$$y+700=4\left(x-700\right)\ \ \ \ \ \ -----\ eqn\ ii$$
$$From\ i,\ x+700=2y-1400$$
$$x=2y-1400-700$$
$$x=2y-2100\ \ \ \ \ -----\ eqn\ iii$$
Let's find Y (i.e the number of car entering).
$$from\ ii,\ y+700=4x-2800$$
substitute value for x derived in eqn iii
$$Therefore,\ y+700=4\left(2y-2100\right)-2800$$
$$ y+700=8y-8400-2800$$
$$ y=8y-8400-2800-700$$
$$-7y=-11900$$
Divide both side by 7
$$Then,\ y=1700$$

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GMAT/MBA Expert

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BTGmoderatorLU wrote:
Source: 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
We can PLUG IN THE ANSWERS, which represent the number of cars in the left lane.

Answer choice C: 1700
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.
After 700 cars are diverted, the number of cars entering the left lane = 1700-700 = 1000.
Since the number of cars entering the right lane is twice the number entering the left lane, the number of cars entering the right lane = 2*1000 = 2000.
Thus, prior to the diversion of the 700 cars, the number of cars in the right lane = 1000-700 = 1300.

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.
After 700 cars are diverted, the number of cars entering the right lane = 1300-700 = 600 and the number of cars entering the left lane = 1700+700 = 2400.
Left lane/right lane = 2400/600 = 4.
Success! The number of cars entering the left lane is 4 times as great as the number of cars entering the right lane.

The correct answer is C.

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