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

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

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

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

Bunuel · Accepted Answer

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.

BrentGMATPrepNow · Answer

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

Cheers,
Brent

bytatia · Answer

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

DmitryFarber · Answer

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.

ScottTargetTestPrep · Answer

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.

hero_with_1000_faces · Answer

Ans: 96 * 3 = 288; 1000 million = 1 billion so next step is 2880*10 ( as 100 million * 10 = 1000 million = Billion)

energetics · Answer

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

Kinshook · Answer

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

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

IMO C

mimajit · Answer

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

ueh55406 · Answer

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.

GMATCoachBen · Answer

Video solution here (2:00):

https://www.youtube.com/watch?v=ZtMXHEONwE0

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