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75% of the guestrooms at the Stagecoach Inn have a queen-siz [#permalink]
13 Jan 2013, 14:38

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Difficulty:

35% (medium)

Question Stats:

70% (02:48) correct
30% (01:46) wrong based on 200 sessions

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 ?

Re: PS: Overlapping sets [#permalink]
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%.

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

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

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

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.

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

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

Answer = E

Attachments

answer.png [ 4.54 KiB | Viewed 242 times ]

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Re: 75% of the guestrooms at the Stagecoach Inn have a queen-siz
[#permalink]
06 Aug 2014, 02:35