Al, Pablo, and Marsha shared the driving on a 1,500-mile trip. Which

Its these kind of mistakes which may cause to be the difference between a 750 and an average score

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.

Going by process of Elimination

Lets take (2) --> It only indicates that Marsha drove 450 km so the remaining distance of 1500 - 450 could be distributed anyway between Al and Pablo. Clearly not sufficient

Taking (1) Let speeds of Pablo = p , time = t. Alone it is clearly insufficient as there are 2 variables and one equation so multiple solutions possible.
Pooling up with (2) ,
1050 = p*t + (p -5)*(t+1)


Since this has two variables and only equation , it can infinite results so Not sufficient.


Bunuel - is my thought process correct ?

1. no info about Marsha. just provided the outline about relation. Hence Not suff.

2. only info about Marsha.. marsha drove 450miles. no info abt others.

combining... aside to marsha 450... no proper info abt divided distance calculation for Al & pablo.

Hence E

I just did this question, and I picked C.

If you know that there was 1050 miles to go, Pablo's speed was 5 miles faster, and Al drive for an hour longer. why can't you solve it?
Al's speed was about = 52.9 mph at 10 hours, and pablos was about 57.9 for 9 hours? That meets all the criteria?

let Speed of A, P and M be SA, SP and SM resp.
& time taken by A, P and M be TA, TP and TM resp.
distance covered by A + distance covered by P + distance covered by M = Total Distance

SA*TA + SP*TP + SM*TM = 1500 --------(1)

To determine : which value is greater among SA*TA , SP*TP & SM*TM

Statement(1) : TA=TP + 1 , SA= SP-5 ; substitute in (1) >> insufficient
Statement(2) : TM=9 , SM =50 ; SM*TM = 450
substitute in (1) : SA*TA + SP*TP = 1050
at this point we have many combinations of SA*TA & SP*TP : can not compare the values >> insufficient

Combining (1) & (2) , we still can't determine the individual values.

Ans : E

Hope this helps. Basically, at the end we have 1 equations with 2 unknowns of Rate and Time. If we knew one of them we could solve. But we don't
A= Al
P= Pablo
M= Marsha
D= Distance
R= Rate
T= Time
D1=Pablo's distance
D2= Marsha's distance
D3 = Al's distance
R2= Marsha's rate (which we don't ever need)
T2 = Marsha's time
Al's Rate and time can be defined in terms of Pablo
R= Pablo's Rate
T= Pablo's Time

Physics Formula Distance = Rate X Time.

We need to determine who (Al, Pablo and Marsha) drove the greatest distance of the 1,500-mile trip.
If we know one person had driven more than ½ the distance of the entire trip, i.e., 750 miles, then he or she must be the person who drove the greatest distance. On the other hand, if we know one person had driven less than ⅓ the distance of the entire trip, i.e., 500 miles, then he or she can’t be the person who dove the the greatest distance.

Statement One Alone:

Al drove 1 hour longer than Pablo but at an average rate of 5 miles per hour slower than Pablo.

Since we don’t know anything about Marsha, statement one alone is not sufficient to answer the question.

Statement Two Alone:

Marsha drove 9 hours and averaged 50 miles per hour.

We see that Marsha drove 9 x 50 = 450 miles. Since this is less than 500 miles, we know Marsha can’t be the person who drove the greatest distance. So either Al or Pablo is the person who drove the greatest distance. However, since we don’t know which one that is, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From the two statements, we see that Al and Pablo together drove 1,050 miles. If we let r = the average rate Al drove and t = the time he drove, we can create the equation:

rt + (r + 5)(t - 1) = 1,050

However, there are two unknowns in this equation, so we can’t determine who (Al or Pablo) drove a greater distance.

For example, suppose first that Al drove for 5 hours. Then, Pablo drove for 4 hours and we have

5r + 4(r + 5) = 1050

9r + 20 = 1050

9r = 1030

r ≈ 114 mph

Thus, Al drives approximately 5 x 114 = 570 miles and Pablo drives 1050 - 570 = 480 miles. In this scenario, Al drives further than Pablo.

On the other hand, suppose that Al drives for 15 hours. Then, Pablo drives for 14 hours and we have

15r + 14(r + 5) = 1050

29r + 70 = 1050

29r = 980

r ≈ 33 mph

Thus, Al drives approximately 15 x 33 = 495 miles and Pablo drives 555 miles. In this scenario, Pablo drives further than Al.

Answer: E

I feel this is one of the most difficult GMAT Quant questions.

C vs E?

Distance covered by A +Distance Covered by P=1050
(Speed A * Time A) + (Speed P * Time P)=1050

If Time P=1.00001, Time A= 0. 00001
(Speed A * 0. 00001) + (Speed A-5 * 1.00001)=1050
Here, we can find out Speed A.

Whatever the value of Speed A, Distance covered by A will be very minimal because Distance covered by A= Speed A * 0. 00001 (i.e. a very small number ). The remaining distance is covered by P. So, P has covered greater distance.

Similarly, if Speed A=5.000001, Speed A=0.000001
(5.000001 * Time A) + (0.000001 * Time A+1)=1050
Here, we can find out Time A.

Whatever the value of Time A, Distance covered by P will be very minimal because Distance covered by P= Time A+1 * 0. 0.000001 (i.e. a very small number ). The remaining distance is covered by A. So, A has covered greater distance.

Insufficient. E is my answer.

Video solution from Quant Reasoning starts at 9:34
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Al, Pablo, and Marsha shared the driving on a 1,500-mile trip. Which of the three drove the greatest distance on the trip?

(1) Al drove 1 hour longer than Pablo but at an average rate of 5 miles per hour slower than Pablo.

Statement 1 is clearly insufficient as we don't have any info about Marsha.

(2) Marsha drove 9 hours and averaged 50 miles per hour.

Statement 2 is also insufficient as there is no details given about Al and Pablo

Lets try to combine both statements.

Distance traveled by Marsha = 9 * 50 = 450 miles.

Distance traveled by Al and Pablo = 1000- 450 = 1050 miles.

If the time taken by Pablo is \( t\) hours, then the time taken by Al is \(t+1\) hours.
It's also given that if average speed of Pablo is \(S\) miles/hour then the average speed of Al is \(S-5\) miles/hours

Distance covered by Pablo = Speed * time = \(S*t\)
Distance covered by Al = \((S -5 )* (t+1)\)

\(S*t + (S -5 )* (t+1) = 1050\)

Since we have 2 variables and a single equation, we will not be able to S and t. That means we cannot compare the distance covered Al, Pablo, and Marsha.

Option E is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME

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