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# A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from

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Joined: 25 Dec 2018
Posts: 148
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from  [#permalink]

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06 Jan 2019, 10:40
3
00:00

Difficulty:

75% (hard)

Question Stats:

56% (03:30) correct 44% (02:43) wrong based on 31 sessions

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A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from 25 to 180 were occupied and the rest were vacant. Two attendants, Kris and Michel, were given the duty of room service of occupied rooms. Each room numbered multiple of 3 was assigned to Kris and each room numbered multiple of 4 was given to Michel. If the rooms which were common for Kris and Michel, and rest of the unassigned occupied rooms were assigned to a third attendant named George, how many rooms were assigned to George?

A. 82
B. 98
C. 99
D. 100
E. 91
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Joined: 18 Jul 2018
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Concentration: Finance, Marketing
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Re: A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from  [#permalink]

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06 Jan 2019, 22:23
Total number of occupied rooms = 180-25+1 = 156
Multiple of 3 for Kris = 27 to 180. Number of rooms = (180-27)/3 + 1 = 52.
Multiple of 4 for Michel = 28 to 180. Number of rooms = (180-28)/4 + 1 = 39.
Rooms common for both Kris and Michel = LCM(3,4) = Multiple of 12 from 25 to 180, i.e, 36 to 180. = (180-36)/12 + 1 = 13.
Number of rooms for George = 156-52-39+13 = 78.

akurathi12, Are the options correct?
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A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from  [#permalink]

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Updated on: 07 Jan 2019, 02:09
2
Afc0892 wrote:
Rooms common for both Kris and Michel = LCM(3,4) = Multiple of 12 from 25 to 180, i.e, 36 to 180. = (180-36)/12 + 1 = 13.
Number of rooms for George = 156-52-39+13 = 78.

13 rooms are common to both Kris and Michel. So Kris served 52-13=39 rooms and Michel served 39-13=26 rooms.
George served=156-39-26=91 rooms.

Hope this helps.

Correct me if I am wrong.

Originally posted by Mahfuz1469 on 06 Jan 2019, 23:52.
Last edited by Mahfuz1469 on 07 Jan 2019, 02:09, edited 1 time in total.
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Re: A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from  [#permalink]

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07 Jan 2019, 01:59
2
Mahfuz1469 wrote:
Afc0892 wrote:
Rooms common for both Kris and Michel = LCM(3,4) = Multiple of 12 from 25 to 180, i.e, 36 to 180. = (180-36)/12 + 1 = 13.
Number of rooms for George = 156-52-39+13 = 78.

13 rooms are common to both Kris and Michel. So Kris served 52-13=39 rooms and Michel served 39-26=13 rooms.
George served=156-39-26=91 rooms.

Hope this helps.

Correct me if I am wrong.

I believe you meant to type Michael served 39-13=26, not 39 - 26=13,that would make sense!

Posted from my mobile device
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A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from  [#permalink]

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07 Jan 2019, 02:05
1
Mahfuz1469 wrote:
Afc0892 wrote:
13 rooms are common to both Kris and Michel. So Kris served 52-13=39 rooms and Michel served 39-26=13 rooms.
George served=156-39-26=91 rooms.

Hope this helps.

Correct me if I am wrong.

I believe you meant to type Michael served 39-13=26, not 39 - 26=13,that would make sense!

Posted from my mobile device

Yeah. Sorry for my silly mistake. Thank you for your correction.
Joined: 25 Dec 2018
Posts: 148
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
Re: A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from  [#permalink]

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07 Jan 2019, 09:31
1
Mahfuz1469 wrote:
Afc0892 wrote:
Rooms common for both Kris and Michel = LCM(3,4) = Multiple of 12 from 25 to 180, i.e, 36 to 180. = (180-36)/12 + 1 = 13.
Number of rooms for George = 156-52-39+13 = 78.

13 rooms are common to both Kris and Michel. So Kris served 52-13=39 rooms and Michel served 39-13=26 rooms.
George served=156-39-26=91 rooms.

Hope this helps.

Correct me if I am wrong.

Your approach is correct. OA also same
Re: A hotel had 180 rooms numbered from 1 to 180. The rooms numbered from   [#permalink] 07 Jan 2019, 09:31
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