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Allison always leaves her office at 5.00pm and reaches her

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Allison always leaves her office at 5.00pm and reaches her

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Allison always leaves her office at 5.00pm and reaches her hotel in an hour, while Brittany leaves the same hotel sometime after 5, meets Allison and reaches the same office at 6.00pm. On Wednesday, just when Brittany met Allison, she realized she had left her laptop. So she went back to the hotel, picked up her laptop and reached the office late. If Allison and Brittany always travel at constant rates, and it took Brittany exactly five minutes to retrieve her laptop between arriving at the hotel and departing again, at what time did Brittany reach the office on Wednesday?

1) When Allison and Brittany meet each day, Allison has already covered exactly 2/3rd of the distance between the hotel and office.
2) Brittany always leaves the hotel at exactly 5.30pm.

The OA is D

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Allison always leaves her office at 5.00pm and reaches her hotel in an hour, while Brittany leaves the same hotel sometime after 5, meets Allison and reaches the same office at 6.00pm. On Wednesday, just when Brittany met Allison, she realized she had left her laptop. So she went back to the hotel, picked up her laptop and reached the office late. If Allison and Brittany always travel at constant rates, and it took Brittany exactly five minutes to retrieve her laptop between arriving at the hotel and departing again, at what time did Brittany reach the office on Wednesday?

(1) When Allison and Brittany meet each day, Allison has already covered exactly 2/3rd of the distance between the hotel and office.

(2) Brittany always leaves the hotel at exactly 5.30pm.
Statement 2: Brittany always leaves the hotel at exactly 5.30pm.
To see the situation more clearly, plug in a value for the distance between the hotel and the office.
Let the distance = 6 miles.

Since Allison takes 1 hour -- from 5 to 6pm -- to travel the entire distance, Alison's rate = d/t = 6/1 = 6 miles per hour.
Since Brittany takes 1/2 hour -- from 5:30 to 6pm -- to travel the entire distance, Brittany's rate = d/t = 6/(1/2) = 12 miles per hour.
When the two travel toward each other, Brittany's rate : Allison's rate = 12:6 = 2:1.
Implication:
Of every 2+1=3 miles that are traveled when Brittany and Allison travel toward each other, Brittany will travel 2 miles and Allison will travel 1 mile.

Thus:
From 5pm to 5:30pm, the distance traveled by Allison alone = rt = 6(1/2) = 3 miles.
At this point, 3 miles remain between Allison and Brittany.
When Brittany and Allison travel toward each other starting at 5:30pm, Brittany will travel 2 of the 3 miles between them, as noted above.
Implication:
When Brittany returns for her laptop, she must travel 2 miles back to the hotel.
Then, to reach the office, she must travel the entire 6 miles.
Thus, the total distance traveled by Brittany = 2+2+6 = 10 miles.
Time for Brittany to travel 10 miles = d/r = 10/12 = 5/6 of an hour.
Since Brittany leaves at 5:30pm -- and she requires 5 minutes to retrieve the laptop -- the time that Brittany reaches the office = 5:30pm + 5/6 of an hour + 5 minutes = 6:25pm.
SUFFICIENT.

Statement 1: Usually, when Allison and Brittany meet, Allison has already covered 2/3rd of the distance between the hotel and office.
From Statement 2:
From 5pm to 5:30pm, the distance traveled by Allison alone = rt = 6(1/2) = 3 miles.
At this point, 3 miles remain between Allison and Brittany.
When Brittany and Allison travel toward each other starting at 5:30pm, Brittany will travel 2 of the 3 miles between them, as noted above.


Thus, the distance traveled by Brittany = (2/3)(3) = 2 miles, implying that the total distance traveled by Allison = 6-2 = 4 miles.
Implication:
Since Allison travels 4/6 = 2/3 of the distance between the hotel and the office, Statement 1 implies the same information as Statement 2.
Thus -- like Statement 2 -- Statement 1 is SUFFICIENT.

The correct answer is D.

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Mitch Hunt
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