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75% of the guestrooms at the Stagecoach Inn have a queensiz [#permalink]
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Updated on: 14 Jan 2013, 01:39
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75% of the guestrooms at the Stagecoach Inn have a queensized bed, and each of the remaining rooms has a kingsized bed. Of the nonsmoking rooms, 60% have a queensized bed. If 10% of the rooms at the Stagecoach Inn are nonsmoking rooms with kingsized beds, what percentage of the rooms permit smoking ? A. 25% B. 30% C. 50% D. 55% E. 75%
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Originally posted by Rock750 on 13 Jan 2013, 15:38.
Last edited by Bunuel on 14 Jan 2013, 01:39, edited 1 time in total.
Renamed the topic and edited the question.



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Re: PS: Overlapping sets [#permalink]
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14 Jan 2013, 00:34
Rock750 wrote: 75% of the guestrooms at the Stagecoach Inn have a queensized bed, and each of the remaining rooms has a kingsized bed. Of the nonsmoking rooms, 60% have a queensized bed. If 10% of the rooms at the Stagecoach Inn are nonsmoking rooms with kingsized 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 NonSmoking 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 queensiz [#permalink]
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28 Jan 2013, 10:43
Rock750 wrote: 75% of the guestrooms at the Stagecoach Inn have a queensized bed, and each of the remaining rooms has a kingsized bed. Of the nonsmoking rooms, 60% have a queensized bed. If 10% of the rooms at the Stagecoach Inn are nonsmoking rooms with kingsized 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 queensiz [#permalink]
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28 Mar 2014, 03:58
akhilbajaj wrote: Rock750 wrote: 75% of the guestrooms at the Stagecoach Inn have a queensized bed, and each of the remaining rooms has a kingsized bed. Of the nonsmoking rooms, 60% have a queensized bed. If 10% of the rooms at the Stagecoach Inn are nonsmoking rooms with kingsized 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 queensiz [#permalink]
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28 Mar 2014, 09:36
gauravsoni wrote: akhilbajaj wrote: Rock750 wrote: 75% of the guestrooms at the Stagecoach Inn have a queensized bed, and each of the remaining rooms has a kingsized bed. Of the nonsmoking rooms, 60% have a queensized bed. If 10% of the rooms at the Stagecoach Inn are nonsmoking rooms with kingsized 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. The rightmost columns and the bottom rows are the sums of preceding boxes. Since 75% of the rooms have a queensized bed, and each of the remaining rooms has a kingsized bed, the the percentage of the rooms that have a kingsized bed is 10075=25. Similarly, if x is the percentage of nonsmoking rooms and 60% of that or 0.6x is nonsmoking rooms with a queensized bed, then x0.6x=0.4x is the percentage of nonsmoking rooms with a kingsized bed. Hope it's clear.
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Re: 75% of the guestrooms at the Stagecoach Inn have a queensiz [#permalink]
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04 Aug 2014, 04:02
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 nonsmoke = 10 Rooms. 60 % of nonsmoke rooms have queen size. So the rest (40 %) must have a king size bed. This means that 10 non smoking rooms are 40 % of nonsmoking 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 queensiz [#permalink]
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06 Aug 2014, 03:35
Rock750 wrote: 75% of the guestrooms at the Stagecoach Inn have a queensized bed, and each of the remaining rooms has a kingsized bed. Of the nonsmoking rooms, 60% have a queensized bed. If 10% of the rooms at the Stagecoach Inn are nonsmoking rooms with kingsized 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 \(\frac{60}{100} (100x) + 10 = 100x\) x = 75% Answer = E
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Re: 75% of the guestrooms at the Stagecoach Inn have a queensiz [#permalink]
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18 Jul 2015, 00:40
Information about no of queen & king size beds is of no use for the solution.



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75% of the guestrooms at the Stagecoach Inn have a queensiz [#permalink]
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20 Mar 2017, 23:25
Rock750 wrote: 75% of the guestrooms at the Stagecoach Inn have a queensized bed, and each of the remaining rooms has a kingsized bed. Of the nonsmoking rooms, 60% have a queensized bed. If 10% of the rooms at the Stagecoach Inn are nonsmoking rooms with kingsized beds, what percentage of the rooms permit smoking ?
A. 25% B. 30% C. 50% D. 55% E. 75% OFFICIAL SOLUTION This is an overlapping sets problem, which can be solved most efficiently by using a double set matrix. Our first step in using the double set matrix is to fill in the information given in the question. Because there are no real values given in the question, the problem can be solved more easily using 'smart numbers'; in this case, we can assume the total number of rooms to be 100 since we are dealing with percentages. With this assumption, we can fill the following information into our matrix: There are 100 rooms total at the Stagecoach Inn. Of those 100 rooms, 75 have a queensized bed, while 25 have a kingsized bed. Of the nonsmoking rooms (let's call this unknown n), 60% or .6n have queensized beds. 10 rooms are nonsmoking with kingsized beds. Let's fill this information into the double set matrix, including the variable n for the value we need to solve the problem: In a doubleset matrix, the first two rows sum to the third, and the first two columns sum to the third. We can therefore solve for n using basic algebra: 10 + .6n = n 10 = .4n n = 25 We could solve for the remaining empty fields, but this is unnecessary work. Observe that the total number of smoking rooms equals 100 – n = 100 – 25 = 75. Recall that we are working with smart numbers that represent percentages, so 75% of the rooms at the Stagecoach Inn permit smoking. The correct answer is E.
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Re: 75% of the guestrooms at the Stagecoach Inn have a queensiz [#permalink]
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21 Mar 2017, 02:39
Rock750 wrote: 75% of the guestrooms at the Stagecoach Inn have a queensized bed, and each of the remaining rooms has a kingsized bed. Of the nonsmoking rooms, 60% have a queensized bed. If 10% of the rooms at the Stagecoach Inn are nonsmoking rooms with kingsized beds, what percentage of the rooms permit smoking ?
A. 25% B. 30% C. 50% D. 55% E. 75% let the total rooms be 100 no. of queen sized bedroom = 75 no. of king sized bedroom = 25 let the non smoking room be x smoking room = 100x queen sized non smoking = 0.6x according to later statement no. of king sized non smoking = 10 king sized non smoking = 0.4x = 10 x = 25 smoking rooms = 75 percentage = 75/100 * 100 = 75%




Re: 75% of the guestrooms at the Stagecoach Inn have a queensiz
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