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A certain hotel has 1,400 single rooms and 420 double rooms.

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A certain hotel has 1,400 single rooms and 420 double rooms.

by AAPL » Wed Mar 13, 2019 3:05 am

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GMAT Paper Tests

A certain hotel has 1,400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?

A. 65
B. 70
C. 80
D. 90
E. 265

OA B
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by Brent@GMATPrepNow » Wed Mar 13, 2019 5:29 am
AAPL wrote:GMAT Paper Tests

A certain hotel has 1,400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?

A. 65
B. 70
C. 80
D. 90
E. 265

OA B
The hotel has 1,400 single rooms, and one person can clean a single room every 15 minutes
So, one person can clean 4 single rooms in ONE HOUR
In other words, it takes 1 WORKER HOUR to clean 4 single rooms

1400/4 = 350
So, it takes 350 WORKER HOURS to clean 1400 rooms

The hotel has 420 double rooms, and one person can clean a double room every 20 minutes
So, one person can clean 3 double rooms in ONE HOUR
In other words, it takes 1 WORKER HOUR to clean 3 double rooms

420/3 = 140
So, it takes 140 WORKER HOURS to clean 420 double rooms

How many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?
350 + 140 = 490
So, 490 WORKER HOURS are required to clean ALL of the room.

490/7 = 70.
So, 70 workers are needed.

Answer: B

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by Scott@TargetTestPrep » Fri Mar 15, 2019 4:47 am
AAPL wrote:GMAT Paper Tests

A certain hotel has 1,400 single rooms and 420 double rooms. Each room is cleaned by one person. If one person can clean a single room every 15 minutes and a double room every 20 minutes, how many cleaning persons are needed to clean all the rooms if each person works for exactly 7 hours?

A. 65
B. 70
C. 80
D. 90
E. 265

OA B
It takes 1400 x 1/4 = 350 hours to clean the single rooms and 420 x 1/3 = 140 hours to clean the double rooms, for a total time of 490 hours. We can let n = the number of workers and create the equation:

7n = 490

n = 70

Answer: B

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by [email protected] » Fri Mar 15, 2019 9:59 am
Hi camitava,

This is essentially a rate question. Here's how to solve it:

Single rooms take one person 15 minutes to clean and double rooms take one person 20 minutes to clean.

15 mins. = 1/4 hour
20 mins. = 1/3 hour

With 1400 single rooms x 1/4 hour = 350 hours of total work for 1 person
With 420 double rooms x 1/3 hour = 140 hours of total work for 1 person

For ALL the rooms, we have a total of 350 + 140 = 490 hours of total work for 1 person

To get the work done in 7 hours, we'll need 490/7 = 70 workers

Final Answer: B

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