Problem Solving

Hi souma730,

This question can be solved with algebra or by TESTing THE ANSWERS. Here's how you can TEST THE ANSWERS:

We're told that both the left and right lanes receive a constant number of cars per hour.

We're also told two pieces of information based on hypotheticals:
1) If 700 cars per hour were transferred from the left lane to the right lane, then the number of cars in the right lane would be DOUBLE the number in the left.
2) If 700 cars per hour were transferred from the right lane to the left lane, then the number of cars in the left lane would be FOUR TIMES the number in the left.

We're asked how many cars enter the left lane per hour.

Let's TEST Answer B....
If....
1500 cars enter the left lane per hour, then (per the 1st hypothetical) the number entering the right lane would be 900 per hour
1500 - 700 = 800
900 + 700 = 1600
Right lane is DOUBLE the left lane

However, these values (1500 and 900) do NOT match the information in the second hypothetical:
900 - 700 = 200
1500 + 700 = 2200
Left lane is 11 TIMES the right lane
Eliminate Answer B

We need more cars in the left lane (to increase the number of cars in the right lane), but the answers are sufficiently "spaced out", that we probably won't need that many more...

Next, let's TEST Answer C...
If....
1700 cars enter the left lane per hour, then (per the 1st hypothetical) the number entering the right lane would be 1300 per hour
1700 - 700 = 1000
1300 + 700 = 2000
Right lane is DOUBLE the left lane

These values (1700 and 1300) ALSO match the information in the second hypothetical:
1700 + 700 = 2400
1300 - 700 = 600
Left lane is 4 TIMES the right lane

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

souma730 wrote: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

Let L = # of cars that enter left lane per hour
Let R = # of cars that enter right lane per hour

If 700 cars per hour were diverted from the left lane to the right lane...
So, L - 700 = cars per hour in the left lane
And R + 700 = cars per hour in 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
So, 2(L - 700)= R + 700

----------------------
If 700 cars per hour were diverted from the right lane to the left lane...
So, L + 700 = cars per hour in the left lane
And R - 700 = cars per hour in the right 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
So, L + 700= 4(R - 700)
-----------------

We now have the following system:
2(L - 700)= R + 700
L + 700= 4(R - 700)

Expand and simplify to get:
2L - 2100 = R
L + 3500 = 4R

Multiply blue equation by 4 to get:
8L - 8400 = 4R
L + 3500 = 4R

Now that both equations are set equal to 4R, we can write the following:
8L - 8400 = L + 3500
Rearrange: 7L = 11,900
Solve: L = 1700
Answer: C

Cheers,
Brent