75% of the guestrooms at the Stagecoach Inn have a queen-siz : GMAT Problem Solving (PS)
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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]

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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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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
Attachments

Document1.pdf [20 KiB]

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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink]

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28 Jan 2013, 09:43
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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%

Attachments

answer.png [ 3.76 KiB | Viewed 5573 times ]

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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink]

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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%

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]

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28 Mar 2014, 08:36
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%

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

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]

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04 Aug 2014, 03:02
Let total number of rooms be 100.

Then number of rooms with
king size: 25
queen size: 75

10 % of total are rooms with king size and non-smoke = 10 Rooms.
60 % of non-smoke rooms have queen size. So the rest (40 %) must have a king size bed. This means that 10 non smoking rooms are 40 % of non-smoking rooms, hence 60 % of non smoking rooms are 15 rooms. This means that 25 rooms are non smoking rooms and 75 are smoking rooms. The answer is E.

Question is quite wordy...for a non native speaker difficult to understand.
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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink]

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06 Aug 2014, 02:35
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%

Refer diagram below:

Say total rooms = 100

We require to find value of "x" (Shaded in Green)

Setting up equation from values calculated in table

$$\frac{60}{100} (100-x) + 10 = 100-x$$

x = 75%

Attachments

answer.png [ 4.54 KiB | Viewed 3208 times ]

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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink]

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17 Jul 2015, 23:40
Information about no of queen & king size beds is of no use for the solution.
Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz   [#permalink] 17 Jul 2015, 23:40
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