Data Sufficiency

Hi guys,

I'm not sure why both statements are not sufficient, can anyone take me through it?

Thanks,
Maysaa

Al, Pablo, and Marsha shared the driving on a 1,500 mile trip. Which of the 3 drove the greatest distance on the trip?

1. Al drove 1 hr longer than Pablo at an avg rate of 5 mph slower than pablo
2. Marsha drove 9 hrs and averaged 50 mph.

Combining the 2 statements:
Distance driven by Marsha = 50*9 = 450.
Distance traveled by Al and Pablo = 1500 - 450 = 1050.
Let the time for Pablo = t and the time for Al = t+1.
The rate for Pablo is 5mph greater than the rate for Al.
TRY EXTREME CASES.

Case 1: Rate for Pablo = 10mph, rate for Al = 5mph
Since the total distance driven by Pablo and Al is 1050, we get:
10t + 5(t+1) = 1050
15t = 1045
t = 1045/15 ≈ 70, implying that the time for Al ≈ 70+1 ≈ 71.
Distance for Pablo ≈ 10*70 ≈ 700, distance for Al ≈ 5*71 ≈ 355.
Pablo drives the greatest distance.

Case 2: Rate for Pablo = 1045mph, rate for Al = 1040mph
Since the total distance driven by Pablo and Al is 1050, we get:
1045t + 1040(t+1) = 1050.
2085t = 10
t = 10/2085 ≈ 1/200, implying that the time for Al ≈ 1/200 + 1 ≈ 201/200.
Distance for Pablo ≈ 1045(1/200) ≈ 5, distance for Al ≈ 1040(201/200) ≈ 1040.
Al drives the greatest distance.

Since in the first case Pablo drives the greatest distance, but in the second case Al drives the greatest distance, INSUFFICIENT.

The correct answer is E.

Al, Pablo, and Marsha shared the driving on a 1,500 mile trip. Which of the 3 drove the greatest distance on the trip?

1. Al drove 1 hr longer than Pablo at an avg rate of 5 mph slower than Pablo.
2. Marsha drove 9 hrs and averaged 50 mph.

That's a cool question.

You look at Statement 1 and it's obviously insufficient because it says nothing about how much driving Marsha did and there's no way to figure it out.

Statement 2 is insufficient because it doesn't provide a way to figure out how much driving Pablo or Al did.

After figuring all that out, one could EASILY be tempted to jump to conclusions and say that when combined the statements provide sufficient information.

Brent@GMATPrepNow wrote:That's not quite right, Marty. The absence of information about Marsha does not necessarily mean that Statement 1 is not sufficient.

Consider this alternative to Statement 1: The distance Pablo drove is 900 miles greater than the distance he would have driven had his driving time and driving speed been reduced by 50%.

Here, we have no information about Marsha and Al, yet this new statement is definitely sufficient, because it tells us that Pablo drove more than 900 miles. Since Pablo drove more than half of the entire distance, he must have driven the greatest distance.

Cheers,
Brent

While in a way you provided some insight, Brent, in your version, we are indirectly provided with information about Marsha and Al.

Notice I said, "it says nothing about how much driving Marsha did and there is no way to figure it out."

In your version the statement provides information sufficient for figuring out the most either Marsha or Al could have driven.