Problem Solving

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Fri Jul 17, 2020 3:56 am

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

Solution:

Let’s let L be the original number of cars that get in the left lane and R be the original number of cars that get in the right lane.

If we divert 700 cars from the left to the right lane, the number of cars in the left lane will be (L - 700), and the number of cars in the right lane will be (R + 700). The result is that there are now twice the number of cars in the right lane as are in the left lane. We can express this as:

2(L - 700) = R + 700

2L - 1400 = R + 700

2L - R = 2100 (Eq. 1)

Now, if we divert 700 cars from the right to the left lane, the number of cars in the right lane will be (R - 700), and the number of cars in the left lane will be (L + 700). The result is that there are now four times the number of cars in the left lane as are in the right lane. We can express this as:

L + 700 = 4(R - 700)

L + 700 = 4R - 2800

L - 4R = -3500 (Eq. 2)

Multiplying Eq 1 by -4 and adding the two equations, we get:


-8L + 4R = -8400 (new Eq 1)
L - 4R = -3500 (Eq 2)

-7L = -11900

L = 1700

Answer: C