Every hour, the same number of cars travels down a highway that splits

Question

Every hour, the same number of cars travels down a highway that splits into two directions. A constant number of these cars turns left and a different number turns right. If in the next hour 700 of the cars that normally would have turned left turn right, then there will be twice as many cars that turn right as turn left. Instead, if in the next hour 700 of the cars that normally would have turned right turn left, then there will be four times as many cars that turn left as turn right. How many cars normally turn left each hour?

A. 1,300

B. 1,500

C. 1,700

D. 1,900

E. 2,100

A. 1,300

B. 1,500

C. 1,700

D. 1,900

E. 2,100

TestPrepUnlimited · Answer

Set y as the number of cars that drive down this highway every hour. Set x as the number of cars that turn left. Then normally we have  y - x  cars turning right.

First equation: In this scenario we have  x - 700  left and  y - x + 700  right,  2*(x - 700) = y - x + 700 .  3x - y = 2100 .

Second equation: In this scenario we have  x + 700  left and  y - x - 700  right,  x + 700 = 4*(y - x - 700) .  5x - 4y = -3500 .

Multiply the first equation by 4:  12x - 4y = 8400 , subtract second equation to get  7x = 11900  and  x = 1700 .

Ans: C

RamseyGooner · Answer

Took me 3:23, need to reduce that, but here's what I did :

Let L be the number of cars turning left and R turning right

Case 1: 2(L-700) = R +700 =>2L - R = 2100 ------ 1

Case 2: L + 700 = 4(R - 700) => 4R - L = 3500 ----2

Multiply eqn. 2 with 2 and add the resultant with eqn. 1

L cancels, left with 7R = 9100; R = 1300

Substitute R in any eqn, we get L = 1700

~R

CrackverbalGMAT · Answer

This is a lengthy word problem where the sheer volume of words can put off a lot of test takers. It is therefore important to focus on the important details – numbers, relationships etc., - and not worry too much about reading all the words in the question. In short, in word problems, focus on understanding the big picture.

What’s the big picture here in this question? There’s a road that splits into two; every hour, a constant number of vehicles turn left and right at this junction. This gives us two variables. Then, there are two hypothetical situations given which help us develop equations involving the variables. A classical word problem.

However, instead of the traditional approach of taking variables, let us work with the answer options. When options are clear 
numbers, it makes sense for you to try them, especially if you have got overwhelmed by the question statement.

In back-solving, we start with C. By doing this, we are saying that 1700 cars normally turn left every hour. In the next hour, 700 of these 1700 cars turned right instead of left; this means 1000 cars turned left. But, we have been told that the number of cars that turned right (as a result of this shift) is double the number of cars that turned left. Therefore, the number of cars that turned right should be 2000.

Of these 2000, let’s not forget that 700 cars were originally supposed to turn left. Therefore, the number of cars that normally turn right has to be 1300.

How can I ensure that option C is my answer? Well, the question actually gives us one more constrain to cross verify.

We know that 1700 cars normally turn left and 1300 cars normally turn right. In the second scenario, 700 of the 1300 cars turned left instead of right. 
So, 2400 cars turned left and only 600 turned right. Number of cars turning left is 4 times of the number of cars turning right, which is what is mentioned in the question.

Therefore, 1700 has to be the number we were looking for.

The correct answer option is C.

Hope that helps!
Aravind B T

bumpbot · Answer

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Every hour, the same number of cars travels down a highway that splits

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Every hour, the same number of cars travels down a highway that splits

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