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# Al, Pablo, and Marsha shared the driving on a 1,500-mile

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Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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Updated on: 25 Aug 2012, 01:55
3
28
00:00

Difficulty:

45% (medium)

Question Stats:

69% (02:15) correct 31% (01:58) wrong based on 1007 sessions

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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.

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

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Originally posted by sondenso on 07 Jun 2008, 19:05.
Last edited by Bunuel on 25 Aug 2012, 01:55, edited 1 time in total.
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Posts: 52297
Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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01 May 2014, 08:37
6
15
himanshujovi wrote:
sondenso wrote:
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.

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

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 ?

Yes, it is.

Though notice that there are certain cases when you CAN solve one equations with two variables. For example, in cases of Diophantine equations (equations whose solutions must be integers only):

eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html
martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html
a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html
joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html
a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html
joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html

Hope it helps.
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Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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01 Aug 2013, 13:17
6
4
Al, Pablo, and Marsha shared the driving on a 1,500-mile trip. Which of the three drove the greatest distance on the trip?

Distance = Rate*time

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

Al Distance: (r-5)*(t+1)
INSUFFICIENT

(2) Marsha drove 9 hours and averaged 50 miles per hour.
Distance = Rate*time
Distance = 50*9
Distance = 450.

Marsha drove 450 miles meaning Al and Pablo drove a combined 950 but we still don't know who drove the most.
INSUFFICIENT

d1+d2=950
(r*t)+[(r-5)*(t+1)]=950
rt+rt+r-5t-5=950
2rt+r-5t=955

There is no further information given about d or t. Unlike other problems where it is possible to plug in other formulas to cancel out variables, plugging in formulas in here will simply lead to the introduction of new variables.
INSUFFICIENT

(E)
##### General Discussion
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Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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01 Aug 2013, 15:27
3
WholeLottaLove wrote:
Marsha drove 450 miles meaning Al and Pablo drove a combined950but we still don't know who drove the most.

Its these kind of mistakes which may cause to be the difference between a 750 and an average score
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Posts: 212
Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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01 May 2014, 07:04
1
1
sondenso wrote:
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.

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

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 ?
Manager
Joined: 07 Apr 2014
Posts: 111
Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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05 Sep 2014, 22:50
sondenso wrote:
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.

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

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
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Posts: 2
Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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17 Mar 2016, 11:42
2
sondenso wrote:
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.

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

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?
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Posts: 23
Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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08 Jan 2017, 08:40
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
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Posts: 73
Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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19 Jun 2017, 18:08
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.
Attachments

AL P M.jpg [ 60.09 KiB | Viewed 9597 times ]

Intern
Joined: 04 Feb 2017
Posts: 13
Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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01 May 2018, 17:00
Bunuel wrote:
himanshujovi wrote:
sondenso wrote:
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.

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

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 ?

Yes, it is.

Though notice that there are certain cases when you CAN solve one equations with two variables. For example, in cases of Diophantine equations (equations whose solutions must be integers only):

http://gmatclub.com/forum/eunice-sold-s ... 09602.html
http://gmatclub.com/forum/martha-bought ... 00204.html
http://gmatclub.com/forum/a-rental-car- ... 05682.html
http://gmatclub.com/forum/joe-bought-on ... 06212.html
http://gmatclub.com/forum/a-certain-fru ... 01966.html
http://gmatclub.com/forum/joanna-bought ... 01743.html

Hope it helps.

Hi Bunuel in such cases where one unique solution exists, is trial and error the only way to arrive at that conclusion? Is there any quicker way to conclude?
In most cases where I have to come to that point and take a call, I end up not having enough time to test multiple conditions before concluding so I end up taking a broad judgement call (that almost always fails).
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Posts: 2830
Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile  [#permalink]

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30 Jul 2018, 10:43
1
1
sondenso wrote:
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.

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

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.

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Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile &nbs [#permalink] 30 Jul 2018, 10:43
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