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Reiko drove from point A to point B at a constant speed, and

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Reiko drove from point A to point B at a constant speed, and

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Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?

1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.

The OA is A

Source: Manhattan Prep

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swerve wrote:
Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?

1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
2) It took Reiko 20 more minutes to drive from A to B than to make the return trip
Test the THRESHOLD.
Since we want to know whether the speed from A to B is greater than 40mph, the threshold here is 40mph.

Statement 1: Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
Let the distance in each direction = 40 miles.
Time to travel the 80 miles there and back at a speed of 80 miles per hour = 1 hour.
If he travels from A to B at the threshold speed -- 40 miles per hour -- then the time from A to B = d/r = 40/40 = 1 hour.
Not possible -- since the TOTAL time is 1 hour, the time FROM A TO B must be LESS than 1 hour.
Thus, the speed from A to B must be GREATER than 40 miles per hour.

Test an extreme case:
Let the distance in each direction = 400 miles.
Time to travel the 800 miles there and back at a speed of 80 miles per hour = 800/80 = 10 hours.
If he travels from A to B at the threshold speed -- 40 miles per hour -- then the time from A to B = 400/40 = 10 hours.
Not possible -- since the TOTAL time is 10 hours, the time FROM A TO B must be LESS than 10 hours.
Thus, the speed from A to B must be GREATER than 40 miles per hour.

The two cases above illustrate the following:
If the speed from A to B is 40 miles per hour, then the TIME FROM A TO B will be equal to the TIME FOR THE ENTIRE TRIP.
Clearly not possible.
Thus, the speed from A to B must be GREATER than 40 miles per hour.
SUFFICIENT.

Statement 2: It took Reiko 20 more minutes to drive from A to B than to make the return trip.
No way to determine the speed from A to B.
INSUFFICIENT.

The correct answer is A.

Take-away:
When the same distance is traveled at two different speeds, the average speed for the entire trip must be LESS THAN TWICE the slower speed.
As the cases in statement 1 illustrate, if the average speed for the entire trip is EQUAL to twice the slower speed, then the TIME TRAVELED AT THE SLOWER SPEED will be equal to the TOTAL TIME FOR THE ENTIRE TRIP.
Clearly not possible.
Since statement 1 indicates that the average speed for the entire trip is 80 miles per hour, if s = the slower speed:
80 < 2s
s > 40.
Since the slower speed is greater than 40 miles per hour, the speed from A to B must be greater than 40 miles per hour.

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Mitch Hunt
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GMATGuruNY@gmail.com

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