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

Question

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.

GMATGuruNY · Answer

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

Jeff@TargetTestPrep · Answer

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@GMATPrepNow · Answer

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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