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

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Manager
Joined: 02 Dec 2012
Posts: 174
Last year, for every 100 million vehicles that traveled on a  [#permalink]

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20 Dec 2012, 08:37
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Difficulty:

5% (low)

Question Stats:

82% (01:18) correct 18% (01:33) wrong based on 788 sessions

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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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Joined: 02 Sep 2009
Posts: 56277
Re: Last year, for every 100 million vehicles that traveled on a  [#permalink]

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20 Dec 2012, 08:42
2
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.

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Joined: 19 Jan 2014
Posts: 25
Re: Last year, for every 100 million vehicles that traveled on a  [#permalink]

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27 May 2014, 20:00
1
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
Manhattan Prep Instructor
Joined: 22 Mar 2011
Posts: 1503
Re: Last year, for every 100 million vehicles that traveled on a  [#permalink]

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28 May 2014, 12:33
2
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]

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07 Jul 2016, 09:30
1
1
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

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Manager
Joined: 02 Jan 2016
Posts: 124
Re: Last year, for every 100 million vehicles that traveled on a  [#permalink]

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14 Mar 2017, 05:51
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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Joined: 12 Sep 2015
Posts: 3848
Re: Last year, for every 100 million vehicles that traveled on a  [#permalink]

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27 Mar 2018, 08:14
1
Top Contributor
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

Cheers,
Brent
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Re: Last year, for every 100 million vehicles that traveled on a  [#permalink]

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12 Apr 2019, 10:16
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:

$$96*30$$ = $$x$$

$$2700+180 → 2880$$ = $$x$$
Re: Last year, for every 100 million vehicles that traveled on a   [#permalink] 12 Apr 2019, 10:16
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