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

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Last year, for every 100 million vehicles that traveled on a [#permalink] New post   20 Dec 2012, 08:37
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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? (1 billion = 1,000,000,000)

(A) 288
(B) 320
(C) 2,880
(D) 3,200
(E) 28,800
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C
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   20 Dec 2012, 08:42
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Walkabout 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? (1 billion = 1,000,000,000)

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


3 billion is 30 times as many as 100 million, so for 3 billion vehicles there would be 30*96=2,880 accidents.

Answer: C.
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   27 Mar 2018, 08:14
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Walkabout 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? (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: 10⁸/96 = (3)(10⁹) /x
Cross multiply to get: (10⁸)(x) = (3)(10⁹)(96)

96 is close enough to 100, so let's replace 96 with 100 to get:
(10⁸)(x) = (3)(10⁹)(100)
or (10⁸)(x) = (3)(10⁹)(10²)
(10⁸)(x) = (3)(10¹¹)
Divide both sides by 10⁸ 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

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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   27 May 2014, 20:00
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Walkabout 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? (1 billion = 1,000,000,000)

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



Hello

The solution above mine is much easier but I didn't catch it under timing so here's how I solved it. (looks easier on paper for canceling out)

(10^8)/96=3x10^9/x
x=(96x3x10^9)/10^8 (cancel out 10^9 and 10^8 you get 10)
x=96x30=2 880
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   28 May 2014, 12:33
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Estimation is helpful here, too. Once you see that you have 30*96, you can say that the answer must be a little less than 30*100, or 3,000. Only C fits.

You could also estimate in advance. The accident rate is 96 per 100 million, which is just under 1 in a million. 3 billion divided by a million is 3,000, so again, the answer should be a bit less than 3,000.
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   07 Jul 2016, 09:30
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Walkabout 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? (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

The answer is C.
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   14 Mar 2017, 05:51
Walkabout 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? (1 billion = 1,000,000,000)

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




Ans: 96 * 3 = 288; 1000 million = 1 billion so next step is 2880*10 ( as 100 million * 10 = 1000 million = Billion)
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   12 Apr 2019, 10:16
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1) Make a ratio and use scientific notation:
\(\frac{96}{10^8}\) = \(\frac{x}{3*10^9}\)

2) Reduce denominator:
\(96\) = \(\frac{x}{3*10}\)

3) Cross multiply and solve:

\(96*30\) = \(x\)

\(2700+180 → 2880\) = \(x\)
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   16 Sep 2019, 08:35
Walkabout 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? (1 billion = 1,000,000,000)

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


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? (1 billion = 1,000,000,000)

100 million vehicles involved in = 96 accidents
3 billion = 3000 million vehicles involved in = 96 * 30 = 2880 accidents

IMO C
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   03 Oct 2019, 03:20
Walkabout 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? (1 billion = 1,000,000,000)

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


This is how i solved

The important thing to note here is 1000 Million makes a 1 Billion

We know that for every 100 Mio we have 96 cars in an accident so for every
1000 Mio we will have 96*10 = 960 cars involved in an accident.

for every 3000 Mio or 3 Billon we will have 960*3 = 2700 +180 = 2880 Cars ans choice C
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Re: Last year, for every 100 million vehicles that traveled on a [#permalink] New post   19 May 2021, 11:04
why bother approximate the closest value when we can just take this as is:

I am taking 10^2 as the common factor for both (because when I'll cross multiply later both of them will cancel out each other, so:

\(100*10^2/96\)=\(300*10^2/x\)

cross multiple and find x. x=288. C looks similar.
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Last year, for every 100 million vehicles that traveled on a [#permalink] New post   24 Dec 2023, 23:57
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Video solution here (2:00):


 
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