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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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07 Jun 2008, 20:05
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Question Stats:

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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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Aug 2012, 02:55, edited 1 time in total.

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08 Jun 2008, 01:17
I will go for E
(1) gives information about Al and PAblo but no relation for Marsha
Insufficient
(2) tells abt Marsho but agin no info abt Al and Pablo
togetehr also no clue
So E is the best option

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

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25 Aug 2012, 02:42
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@Bunuel,
Could you please explain why both the statements together are insufficient.
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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, 14:17
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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?

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)

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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, 16:27
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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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Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile [#permalink]

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01 May 2014, 08:04
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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 ?

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

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01 May 2014, 09:37
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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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05 Sep 2014, 23:50
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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Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile [#permalink]

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02 Oct 2015, 17:30
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Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile [#permalink]

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17 Mar 2016, 12:42
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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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*HELP* Al, Pablo, and Marsha shared the driving on a 1,500-mile trip [#permalink]

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17 Mar 2016, 12:48
1
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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.

The answer has been chosen to be E by several other posts, but I don't know why you can't solve it.

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 Pablo's was about 57.9 for 9 hours? That meets all the criteria?

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

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17 Mar 2016, 13:12
arjuntino 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.

The answer has been chosen to be E by several other posts, but I don't know why you can't solve it.

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 Pablo's was about 57.9 for 9 hours? That meets all the criteria?

Merging topics. please refer to the discussion above.
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Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile [#permalink]

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02 Aug 2016, 06:15
arjuntino 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.

The answer has been chosen to be E by several other posts, but I don't know why you can't solve it.

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 Pablo's was about 57.9 for 9 hours? That meets all the criteria?

Thank you.

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

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08 Jan 2017, 09:40
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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Al, Pablo, and Marsha shared the driving on a 1,500-mile [#permalink]

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19 Jun 2017, 19:08
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 2072 times ]

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

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19 Aug 2017, 06:18
Hi Bunuel,

Many a times, only one equation is sufficient to solve the question as you mentioned in one of your posts. Even I observed the same.

statement 1+2(pablo has an speed of r and drives for t time)
Keeping this information in mind,

I tried to plugin the value in the below equation to find out if Pablo always have the highest speed, but I failed to do this within 2 mins. Is there a faster way to verify that it is not sufficient?
(t+1)(r-5)+tr=1050

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Re: Al, Pablo, and Marsha shared the driving on a 1,500-mile   [#permalink] 19 Aug 2017, 06:18
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