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Last year, for every 100 million vehicles that traveled on..

by swerve » Thu Mar 22, 2018 9:09 am
Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents?

A. 288
B. 320
C. 2,880
D. 3,200
E. 28,800

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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by GMATGuruNY » Thu Mar 22, 2018 9:47 am
swerve wrote:Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents?

A. 288
B. 320
C. 2,880
D. 3,200
E. 28,800
3 billion = 3,000,000,000 = 3*10�
100 million = 100,000,000 = 10�.

The goal is to convert 3*10� vehicles into the correct number of accidents.
Since there are 96 accidents for every 10� vehicles, we get:
(3*10� vehicles) * (96 accidents)/(10� vehicles) = 3*96*10 = 2880 accidents.
In the equation above, the vehicles in red CANCEL OUT, leaving the result in terms of ACCIDENTS.

The correct answer is C.
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by Jeff@TargetTestPrep » Mon Mar 26, 2018 4:52 pm
swerve wrote:Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents?

A. 288
B. 320
C. 2,880
D. 3,200
E. 28,800
To solve, we will set up a proportion. We know that "100 million vehicles is to 96 accidents as 3 billion vehicles is to x accidents". To express everything in terms of "millions", we will use 100 for 100 million and 3,000 for 3 billion since 3 billion = 3,000 million. We can create a proportion:

100/96 = 3,000/x

Cross multiplying gives us:

100x = 3,000 * 96

x = 30 * 96 = 2,880

Answer: C

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by Brent@GMATPrepNow » Tue Mar 27, 2018 7:10 am
swerve wrote:Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents?

A. 288
B. 320
C. 2,880
D. 3,200
E. 28,800

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
We can use equivalent ratios to solve this.
# cars/# accidents: 100,000,000/96 = 3,000,000,000/x
Rewrite with exponents: 10�/96 = (3)(10�) /x
Cross multiply to get: (10�)(x) = (3)(10�)(96)

96 is close enough to 100, so let's replace 96 with 100 to get:
(10�)(x) = (3)(10�)(100)
or (10�)(x) = (3)(10�)(10²)
(10�)(x) = (3)(10¹¹)
Divide both sides by 10� to get: x = (3)(10³) = 3000

We see that both C and D are close to 3000
However, in our calculations, we replaced 96 with 100, so our calculations are a bit HIGHER than they should be. So, the correct answer must be a little smaller than 3000

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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