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MIllion VS Billion

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by oquiella » Sat Oct 10, 2015 1:20 pm
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 invovled in accidents? ( 1 billion= 1,000,000,000)

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


Converting from millions to billions is my weak point in word problems.
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by theCEO » Sat Oct 10, 2015 1:46 pm
oquiella 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 invovled in accidents? ( 1 billion= 1,000,000,000)

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


Converting from millions to billions is my weak point in word problems.
100 million = (10^2)x10^6 = 10^8
3 billion = 3 x 10^9

(3 x 10^9 / 10^8 ) * 96
3 * 10 *96 = 2880

ans = c
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by Brent@GMATPrepNow » Sat Oct 10, 2015 2:28 pm
oquiella 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 invovled in accidents? ( 1 billion= 1,000,000,000)

A. 288
B. 320
C. 2,880
D. 3,200
E. 28,800
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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by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:35 pm
oquiella 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 invovled in accidents? ( 1 billion= 1,000,000,000)

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 can use 3,000 million rather than 3 billion. Creating a proportion, we have:

100/96 = 3,000/x

Cross multiplying gives us:

100x = 3,000 * 96

x = 30 * 96 = 2,880

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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