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Al, Pablo and Marsha shared the driving on a 1,500-mile [#permalink]
11 Jul 2006, 04:51

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E

Difficulty:

35% (medium)

Question Stats:

72% (02:03) correct
28% (01:27) wrong based on 151 sessions

Al, Pablo and Marsha shared the driving on a 1,500-mile trip. Which of the three drove the greatest distance of the trip?

(1) Al drove 1 hour longer than Pablo but at an average rate of 5 miles per hour slower than Pablo. (2) Marsha drove 9 hours and averaged 50 miles per hour.

It is "easy" to see, that both (1) and (2) alone are not sufficient.

Are (1) and (2) together sufficient?

I construct a counterexample.

We know from (2) that Al and Paul drove 1050 miles.

Notation: A = distance driven by Al, P = distance driven by Paul. h(A): hours driven by Al, h(P) = hours driven by Paul. S(A) = speed (Al is the driver), S(P) = speed (when P is the driver).

It seems like (1) & (2) are sufficient until you try to solve, which gives you an equation in Sp& Tp (Speed of Paul and Time for Paul) which is not solvable.

Re: Al, Pablo and Marsha shared the driving on a 1,500-mile [#permalink]
12 Oct 2013, 12:22

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You don't necessarily need too much math for this one.

From (2) we know that Marsha drove 450 miles, meaning that Al and Pablo drove 1050 miles. This tells us that Marsha wasn't the one who drove the greatest distance. But still not sufficient to know who between Al and Pablo drove the most miles.

From (1), consider two extreme scenarios: [Scenario One]: Al drove 1 mph, whereas Pablo drove 6 mph. In this case, even if Al drove an hour longer than Pablo, it was Pablo who drove the greatest number of miles. [Scenario Two]: Al drove 200 mph, whereas Pablo drove 205 mph. In this case, an hour extra driving from Al makes him the one who drove the most distance.

Therefore: Answer E.

I hope that is clear for the ones who avoid math for DS.