Office & Hotel

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Office & Hotel

by manik11 » Thu Nov 19, 2015 4:36 am
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


OA : D
Source : Veritas Prep

I've got no clue how to approach this one.

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Allison and Brittany

by GMATGuruNY » Thu Nov 19, 2015 5:12 am
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.
Last edited by GMATGuruNY on Fri Jan 04, 2019 1:23 pm, edited 3 times in total.
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by MartyMurray » Thu Nov 19, 2015 5:32 am
To get the answer to this one, you need to know something about how fast Brittany travels and how long it takes for her to get from the hotel to the office.

If she travels very fast, she won't be much over five minutes late, because the traveling won't use up much time. If she travels slowly, then in addition to the extra five minutes she spent retrieving her laptop, she will use up a lot of time travelling the extra distance.

Statement 1 tells us that Brittany meets Allison when Allison is 2/3 of the way to the hotel. We know that Allison takes 1 hour to get to the hotel. So Brittany meets Allison at 5:40 PM.

If Allison is 2/3 of the way to the hotel, then at 5:40 PM, Brittany is 1/3 of the way to the office. If she gets there by 6:00 PM, then she goes 2/3 of the way in 20 minutes.

So she Brittany goes 1/3 of the way in 10 minutes, meaning that she leaves at 5:30.

From this we can figure out that Brittany left the hotel ten minutes before meeting Allison, then going back took ten minutes, retrieving her laptop took 5 minutes and she then needed a half hour to get to the office.

I am not even going to calculate the time she arrived. I know that I can and so Statement 1 is sufficient.

Statement 2 tells us that Brittany gets to the office in 1/2 hour. We know that Allison gets to the hotel in 1 hour. By using this we can figure out the following.

Calling the distance D, at 5:30 Allison will be halfway back. So when Brittany leaves, they have to cover 1/2 D in order to meet. We know Allison's rate is D/hour. We know Brittany's rate is 2D/hour. We can figure out when and where they will meet.

I already know from my calculations from Statement 1 that I can now figure out how long it will take for Brittany to get to the office. So Statement 2 is sufficient.

The correct answer is D.
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by Matt@VeritasPrep » Fri Nov 27, 2015 1:49 am
Let's go for a succinct approach.

Suppose the distance from the hotel to the office is 30 miles. Since Allison can get there in one hour, Allison's rate is 30mph.

When Allison and Brittany meet, they will have traveled the entire 30 miles between them: Allison will have done one chunk and Brittany will have done the other chunk.

S1::

Brittany and Allison meet at 5:40. Allison will have traveled 20 miles, so Brittany has traveled the other 10. From here, Brittany would arrive at the office in 20 minutes, since we know she always gets there at 6:00. That means Brittany's rate is 20 miles (the remaining distance) in 20 minutes (the time from 5:40 to 6:00), which translates to a rate of 60 mph; SUFFICIENT.

S2::

Brittany leaves the hotel at 5:30. Since she gets to the office (30 miles away) in 30 minutes, her rate is again 60 mph. This is double Allison's rate, so again we can figure out exactly where they meet, etc. SUFFICIENT.