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# There are 210 rooms in a hotel. All of the rooms are cleaned by

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BSchool Forum Moderator
Joined: 29 Jan 2015
Posts: 1466
Location: India
WE: General Management (Non-Profit and Government)
There are 210 rooms in a hotel. All of the rooms are cleaned by  [#permalink]

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16 Feb 2019, 05:48
1
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Difficulty:

25% (medium)

Question Stats:

76% (01:49) correct 24% (02:15) wrong based on 45 sessions

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There are 210 rooms in a hotel. All of the rooms are cleaned by housekeepers. If each of the housekeepers cleans same number of rooms, how many housekeepers are there?

(1) Each of the housekeepers cleans an odd number of rooms.

(2) The number of the housekeepers is greater than the number of the rooms a housekeeper clean.
Intern
Joined: 07 Jan 2018
Posts: 16
Re: There are 210 rooms in a hotel. All of the rooms are cleaned by  [#permalink]

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16 Feb 2019, 06:36
1
Let number of housekeepers be K. Let number of rooms cleaned by each housekeeper be N
Given N*K=210= 2*3*5*7.

1) Each of the housekeepers cleans an odd number of rooms.
So, N can be 3,5,7,5*7,7*3,5*3,5*7*3.
Insufficient

2)The number of the housekeepers is greater than the number of the rooms a housekeeper clean.
K>N
Insufficient

Combining 1) and 2)
K>N and N is Odd
But by how much is K greater than N (We have two variables and only one equation)?
Insufficient.
Manager
Joined: 11 Mar 2018
Posts: 158
Re: There are 210 rooms in a hotel. All of the rooms are cleaned by  [#permalink]

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19 Feb 2019, 04:17
rohan2345 wrote:
There are 210 rooms in a hotel. All of the rooms are cleaned by housekeepers. If each of the housekeepers cleans same number of rooms, how many housekeepers are there?

(1) Each of the housekeepers cleans an odd number of rooms.

(2) The number of the housekeepers is greater than the number of the rooms a housekeeper clean.

I also considered the case of 210 x 1, that is 210 housekeepers and 1 room per housekeeper.

As far as I can understand it satisfies all conditions of the question.

Intern
Joined: 19 May 2019
Posts: 16
Re: There are 210 rooms in a hotel. All of the rooms are cleaned by  [#permalink]

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26 Sep 2019, 05:33
rohan2345 wrote:
There are 210 rooms in a hotel. All of the rooms are cleaned by housekeepers. If each of the housekeepers cleans same number of rooms, how many housekeepers are there?

(1) Each of the housekeepers cleans an odd number of rooms.

(2) The number of the housekeepers is greater than the number of the rooms a housekeeper clean.

I also considered the case of 210 x 1, that is 210 housekeepers and 1 room per housekeeper.

As far as I can understand it satisfies all conditions of the question.

HI,

There will be another option like 30*7,

In which 30 housekeepers and 7 rooms per house keeper. This also satisfies the both conditions...

And one more 42*5, 42 house keepers and 5 rooms per house keeper satisfies both options.

So even after combining we cannot find a unique solution of how many house keepers are available in hotel?

That's why, the correct answer is option E.

Hope the explanation helps.....
Re: There are 210 rooms in a hotel. All of the rooms are cleaned by   [#permalink] 26 Sep 2019, 05:33
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