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# The faster a car is traveling, the less time the driver

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Joined: 28 May 2015
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Re: The faster a car is traveling, the less time the driver  [#permalink]

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17 Jan 2018, 11:27
VeritasPrepKarishma wrote:
truongynhi wrote:
Hi Karishma,

How could we know that the fatality rate (or the number of fatalities) will increase proportionally with the increase in mileage driven?

In my flawed reasoning, I just simply put the increased denominator, which is the mileage driven (assuming the same number of cars), in the rate formula and consequently concluded that fatality rate increases.

The point is that fatality rate per highway mile driven does not change if the number of miles driven increases. It is something like this:

Say my speed is 60 miles/hr. I maintain this speed. Does it matter whether I drive for 2 hours at this rate or 4 hours at this rate? Will my speed change if I drive more? No, right? When I drive for more hours, the distance I covered increases.

Similarly, fatality rate per highway mile is a rate which will not change with the change in the number of highway miles driven. If more highway miles are driven, the number of fatalities increase.

Passage - If high speed then fatality will surely happen {among other things equal} 'a general truth sort of thing.

Question stem asks why fatality rate decreased inspite of increase in speed ?

Option D says about avg . mileage driven by cars increased. So it means that per car started travelling more on increased speed which in turn signifies that more travel more fatality. So indirectly it is not solving the paradox but rather restating the premise in a different way. Until we dont bring some external factor into picture as has been brought by option B then fatality cannot be reduced because it is bound to happen if travelling more on high speeds.

Now few contributors have expressed doubt that the ratio of FATALITY / MILES DRIVEN has reduced in option D but in thinking they are indirectly assuming that no fatality is taking place by driving more at high speed.

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Re: The faster a car is traveling, the less time the driver  [#permalink]

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31 Jul 2018, 07:47

Average speed = total distance / total time

Since this is a paradox question, let us first understand what is the paradox:

Quote:
The faster a car is traveling, the less time the driver has to avoid a potential accident, and if a car does crash, higher speeds increase the risk of a fatality. Between 1995 and 2000, average highway speeds increased significantly in the United States, yet, over that time, there was a drop in the number ofcar-crash fatalities per highway mile driven by cars.

More speed of car -> Less time a driver has to avoid an accident.
So More speed -> More chance of fatal accidents.

1995 - 2000 : AVERAGE SPEED on highway increased.
So what is expected?
More no of fatal accidents.
But ACTUALLY,
drop in fraction: no of car-crash fatalities / Distance

Option D clearly says: average mileage has increased. Mileage means no of kms travelled per unit consumption of fuel.
If the denominator increases, fraction decreases and hence paradox is resolved.
I considered (B) out of scope since it does not express any variable in my fraction.
Let me know flaws in my understanding.
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31 Jul 2018, 20:58
1
goodyear2013 wrote:
The faster a car is traveling, the less time the driver has to avoid a potential accident, and if a car does crash, higher speeds increase the risk of a fatality. Between 1995 and 2000, average highway speeds increased significantly in the United States, yet, over that time, there was a drop in the number of car-crash fatalities per highway mile driven by cars.

Which of the following, if true about the United States between 1995 and 2000, most helps to explain why the fatality rate decreased in spite of the increase in average highway speeds?

(B) There were increases in both the proportion of people who wore seat belts and the proportion of cars that were equipped with airbags as safety devices.

(D) The average mileage driven on highways per car increased.

Average speed = total distance / total time

Since this is a paradox question, let us first understand what is the paradox:

Quote:
The faster a car is traveling, the less time the driver has to avoid a potential accident, and if a car does crash, higher speeds increase the risk of a fatality. Between 1995 and 2000, average highway speeds increased significantly in the United States, yet, over that time, there was a drop in the number ofcar-crash fatalities per highway mile driven by cars.

More speed of car -> Less time a driver has to avoid an accident.
So More speed -> More chance of fatal accidents.

1995 - 2000 : AVERAGE SPEED on highway increased.
So what is expected?
More no of fatal accidents.
But ACTUALLY,
drop in fraction: no of car-crash fatalities / Distance

Option D clearly says: average mileage has increased. Mileage means no of kms travelled per unit consumption of fuel.
If the denominator increases, fraction decreases and hence paradox is resolved.
I considered (B) out of scope since it does not express any variable in my fraction.
Let me know flaws in my understanding.

adkikani , others have taken your position and I can see why D seems appealing.

The instinct to solve a math question is understandable but misplaced. Some piece of information has been omitted. What is the most direct question to ask about the paradox? What does not fit?

We need a logical, not a mathematical, explanation for what seem to be contradictory facts.

In a paradox CR question, we usually need some "outside" factor to intervene, some omitted information to be given, in order to explain the paradox.

What saved the lives of people who got in car accidents? Logically, that question is the one most connected to the contradiction.

That question is especially pertinent because, see below, there are almost certainly many more accidents now overall.

A paradox involves contradictory elements that are somehow related. Arithmetic alone cannot save lives. Driving more miles cannot save lives.

Maybe the overwhelming majority of drivers suddenly got trained as race car drivers?

Maybe hundreds of thousands of extra roads were built so there were fewer cars on the road at any given time?

Maybe the cars themselves were safer?

If we face a paradox, we should try to "get to the heart" of the contradiction. That is, in order to resolve this paradox, we should try to untangle, to disconnect logically, the fact of increased speed from the gruesome spectacle of human beings who perish in car crashes.

I'm going to change the direction of discussion.

So far I have not seen a heavy emphasis on the distinction between "all crashes" and "fatal crashes."

From the prompt, it is almost certain that the number of car crashes generally has increased:

"the faster a car is traveling, the less time the driver has to avoid a [ANY] potential accident [non-fatal or fatal].

Speeds have increased.

A higher rate of car crashes per mile driven is almost a logical necessity. Speed increases the risk of accidents generally. Further and somewhat separately, speed increases the risk that people will die in those accidents.

Although not stated outright, from the logic of the prompt it is completely reasonable to infer more accidents overall happen now than before speeds increased.

Something intervened to decrease the number of crashes that were fatal.

Something caused fewer people to die in bad car accidents.

The subject matter of answer D is not a substantive causal explanation. More miles driven cannot save lives. More miles driven exerts a mathematically correlational effect on the fatality rate IF and only if the overall number of accidents stayed steady.

An unchanged accident rate is not very likely. Most importantly for future CR paradox questions: more miles driven" is not the "best" explanation for the paradox.

Indeed, the whole fractional analysis involving an increased denominator and thus a decreased numerator simply means that the event "more miles driven" may have DILUTED the death rate.

Diluting the fatality rate is different from causing its decrease -- from causing the number in the numerator, FATAL accidents, to decrease.

The question that resolves the paradox if answered (as in B) is, "What stops people from DYING when they get into car crashes?"

The question that resolves the paradox is not (as in D), "What event dilutes the rate at which people die horrible deaths in car crashes? What event merely scatters the same number of people killed in car crashes across more square miles?"

"Driving more miles" does not cause people to survive otherwise deadly accidents. Seatbelts and airbags prevent death. Seatbelts and airbags cause people to survive otherwise deadly accidents.

Bottom line: an increase in miles driven may correlate with a decrease in overall fatal car crash rate.

Even that correlation is suspect. You assume a steady overall crash rate in the face of evidence to the contrary.

Suppose I hypothetically concede that the overall accident rate stayed steady, such that the arithmetic fatality rate as you have defined it went down. Again, the increased miles themselves did not cause fewer deaths per mile driven.

Increasing the denominator simply results in decreasing the numerator. That result is a math fact, not a way to reconcile and uncouple what seem to be contradictory facts.

Answer D, in other words, cannot rule out more accidents generally, and does not explain fewer deaths per accident per mile specifically.

Logic and math can overlap, but they are not identical. Answer B did not fit into your rate because the more important rate is FATAL crashes / ALL crashes.
THAT rate is the key to the problem.

The best logical explanation for fewer fatalities given identical or increased accident rates generally is in B.
Seat belts and airbags save lives of human beings who are in terrible car accidents.

I hope that analysis helps.

Question: A father and son are in a horrible car crash that kills the dad. The son is rushed to the hospital; just as he’s about to go under the knife, the surgeon says, “I can’t operate — that boy is my son!” Explain.
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The faster a car is traveling, the less time the driver  [#permalink]

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31 Jul 2018, 23:41
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generis interesting question considering the fact this is kinda of a cr question ...hmm if father is dead , i mean he really died in car accident, and son survived... there should be some close relative or simply a mother (in this particular case) in surgeons in place because surgeon says I can’t operate — that boy is my son. so if one of them died, and if surgeon says "I can’t operate — that boy is my son" so that makes me think that surgeon was mother.
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Re: The faster a car is traveling, the less time the driver  [#permalink]

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01 Aug 2018, 05:16

Average speed = total distance / total time

Since this is a paradox question, let us first understand what is the paradox:

Quote:
The faster a car is traveling, the less time the driver has to avoid a potential accident, and if a car does crash, higher speeds increase the risk of a fatality. Between 1995 and 2000, average highway speeds increased significantly in the United States, yet, over that time, there was a drop in the number ofcar-crash fatalities per highway mile driven by cars.

More speed of car -> Less time a driver has to avoid an accident.
So More speed -> More chance of fatal accidents.

1995 - 2000 : AVERAGE SPEED on highway increased.
So what is expected?
More no of fatal accidents.
But ACTUALLY,
drop in fraction: no of car-crash fatalities / Distance

Option D clearly says: average mileage has increased. Mileage means no of kms travelled per unit consumption of fuel.
If the denominator increases, fraction decreases and hence paradox is resolved.
I considered (B) out of scope since it does not express any variable in my fraction.
Let me know flaws in my understanding.

Yes, it is a tricky thing and certainly hard to explain. Though I have tried to do it here: https://www.veritasprep.com/blog/2016/0 ... reasoning/

Also, mileage here has nothing to do with consumption of fuel. It is just the average miles driven per car on highways.
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The faster a car is traveling, the less time the driver  [#permalink]

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04 Aug 2018, 01:06
1
generis wrote:
A father and son are in a horrible car crash that kills the dad. The son is rushed to the hospital; just as he’s about to go under the knife, the surgeon says, “I can’t operate — that boy is my son!” Explain.

The surgeon = Stepfather or stepmother would explain that paradox.
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The faster a car is traveling, the less time the driver  [#permalink]

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Updated on: 04 Aug 2018, 07:34
hazelnut wrote:
generis wrote:
A father and son are in a horrible car crash that kills the dad. The son is rushed to the hospital; just as he’s about to go under the knife, the surgeon says, “I can’t operate — that boy is my son!” Explain.

The surgeon = Stepfather or stepmother would explain that paradox.

hazelnut nice guess

Ok here ia a question for you hazelnut

Gays are becoming increasingly more but they don’t reproduce themselves.

Which helps to resolve paradox ?

Originally posted by dave13 on 04 Aug 2018, 01:32.
Last edited by dave13 on 04 Aug 2018, 07:34, edited 2 times in total.
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04 Aug 2018, 01:44
1
dave13 wrote:
Gays are becoming increasingly more but they don’t reproduce themselves.

Which helps to resolve paradox ?

Gay couple could probably adopt a child.
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Re: The faster a car is traveling, the less time the driver  [#permalink]

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09 Apr 2019, 12:47
Okay based on explainations of VeritasKarishma ma'am and my own reasoning, simply we can say that the argument is dependent on:

#fatality / # of miles travelled

Agreed to it, but there are two equations to the problem

#fatality = k ( positive constant) * Speed

Based on second formula, it can be said for option D that the #fatality will increase making the rate = ( #fatality/ #miles travelled) a constant since both have increased and this might increase the gap in the paradox.

I believe this reasoning is sound.
In option B, we derive one more equation that weakens our second equation ( the relation between fatality and speed) and hence it helps reduce the gap of our paradox
Regards,
Rishav
Re: The faster a car is traveling, the less time the driver   [#permalink] 09 Apr 2019, 12:47

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