Data Sufficiency

Guys ,

Pls help me out..

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.

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient
D) EACH statement ALONE is sufficient
E) Statements (1) and (2) TOGETHER are NOT sufficient.

OAA

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.

This is a THRESHOLD problem.
The question does not ask for Reiko's exact speed from A to B.
Rather, it asks whether Reiko's speed from A to B was beyond a certain THRESHOLD (40mph).

Strategy: TEST the threshold.
See whether it's possible for Reiko to travel from A to B at the threshold speed of 40mph.

Statement 1: Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
Case 1: 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 Reiko 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.

Case 2: 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 Reiko 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.

Here's the 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.