BTGmoderatorLU wrote:Source: Manhattan Prep
Al and Barb shared the driving on a certain trip. What fraction of the total distance did Al drive?
1) Al drove for \(3/4\) as much time as Barb did.
2) Al's average driving speed for the entire trip was \(4/5\) of Barb's average driving speed for the trip.
The OA is C
Say the total distance of the trip is D miles and AL drove d miles out of D miles. We have to get the value of d/D.
Let's take each statement one by one.
1) Al drove for \(3/4\) as much time as Barb did.
No information about the distance. Note that we cannot assume that Aland Barb drove at the same average driving speed for the trip. Insufficient.
2) Al's average driving speed for the entire trip was \(4/5\) of Barb's average driving speed for the trip.
We do not know for how long Al and Barb drove. Insufficient.
(1) and (2) together
From (1), say Al's driving time = 3 hours; thus, Barb's driving time = 4 hours
From (2), say Al's average speed = 40 mph; thus, Barb's average speed = 50 mph
Thus, the distance drove by Al = d = 40*3 = 120 miles and the distance drove by Barb = 50*4 = 200 miles. Thus, D = 120 + 200 = 320 miles
Thus, d/D = 120/200. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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