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75% of the guestrooms at the Stagecoach Inn have a queen-siz

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75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink] New post 13 Jan 2013, 14:38
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75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 10% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking ?

A. 25%
B. 30%
C. 50%
D. 55%
E. 75%
[Reveal] Spoiler: OA

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Last edited by Bunuel on 14 Jan 2013, 00:39, edited 1 time in total.
Renamed the topic and edited the question.
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Re: PS: Overlapping sets [#permalink] New post 13 Jan 2013, 23:34
Rock750 wrote:
75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 10% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking ?

A- 25%
B- 30%
C- 50%
D- 55%
E- 75%



Hi,

Let x be the total no of Guest rooms and y be the total no of Non -Smoking rooms. Based on given information, following matrix can be formed (refer attachment)


Then Questions asks to to find z/x*100
Now from the Condition for Non-Smoking room we get,

0.6y+0.1x=y---> 0.4y=0.1x ---> x=4y i.e z=3y and therefore z/x*100 is 75%.

Thanks
Mridul
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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink] New post 28 Jan 2013, 09:43
Rock750 wrote:
75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 10% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking ?

A. 25%
B. 30%
C. 50%
D. 55%
E. 75%



from the table, we can calculate that % of Non- smoking rooms, x = 25%
Thus, % of Rooms that permit smoking (mrked as "?") = 75%

Answer E
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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink] New post 28 Mar 2014, 02:58
akhilbajaj wrote:
Rock750 wrote:
75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 10% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking ?

A. 25%
B. 30%
C. 50%
D. 55%
E. 75%



from the table, we can calculate that % of Non- smoking rooms, x = 25%
Thus, % of Rooms that permit smoking (mrked as "?") = 75%

Answer E



Hi thanks for the answer.

I am not able to understand as how from 10% you have calculated 0.4X or 25%. Can you please answer.
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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink] New post 28 Mar 2014, 08:36
Expert's post
gauravsoni wrote:
akhilbajaj wrote:
Rock750 wrote:
75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 10% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking ?

A. 25%
B. 30%
C. 50%
D. 55%
E. 75%


Image
from the table, we can calculate that % of Non- smoking rooms, x = 25%
Thus, % of Rooms that permit smoking (mrked as "?") = 75%

Answer E



Hi thanks for the answer.

I am not able to understand as how from 10% you have calculated 0.4X or 25%. Can you please answer.


The rightmost columns and the bottom rows are the sums of preceding boxes.

Since 75% of the rooms have a queen-sized bed, and each of the remaining rooms has a king-sized bed, the the percentage of the rooms that have a king-sized bed is 100-75=25.

Similarly, if x is the percentage of non-smoking rooms and 60% of that or 0.6x is non-smoking rooms with a queen-sized bed, then x-0.6x=0.4x is the percentage of non-smoking rooms with a king-sized bed.

Hope it's clear.
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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz   [#permalink] 28 Mar 2014, 08:36
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