PROBLEM SOLVING

[dell2]

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%

[Frankenstein]

Hi,
Let the number of smoking(s) and non-smoking(n) rooms be 100x and 100y. Let q and k denote queen and king size.
Of the non-smoking rooms, 60% have a queen-sized bed
So, n(100y) -> q(60y) and k (40y)

10% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds
So, 40y = (10/100)(100x+100y) => x=3y

So, % of smoking rooms = 100x/(100x+100y) = x/(x+y) = 3y/(3y+y) = 3/4 = 75%

Hence, E

[cans]

let total =100
75=Q sized bed
25 K sized bed
10: NS (non-smoking) + K sized
let smoking=x
then non smoking=100-x
NS + Q = (60/100)*(100-x) = (3/5)(100-x)
thus total NS = 10 + (3/5)(100-x)
smoking = x
total = x+10+ (3/5)(100-x) = 100
x+70 - 3x/5 = 100
2x/5 = 30
x=75
IMO E

[manpsingh87]

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%

total no. of rooms=100;
qs= queen sized
ks=king sized;
s=smoking
ns=non smoking;

so qs+ks=100;
also s+ns=100;-----1)
now as per the question we have 60% of ns rooms are queen sized therefore remaining 40% of the ns are king sized;
also as per the question;
10%of the total room are non smoking with king sized beds, hence;
40/100(ns)=10/100*100;
40/100(ns)=10;
ns=25;
putting it in 1) we have;
s=100-25;
s=75 hence E

[[email protected]]

Answer is surely E. Also you can also get the answer through the diagram format.
Explanation:


100
Queen - Sized Rooms King - Sized Rooms
75 25
Smoking Rooms Non-Smoking Rooms Smoking Non - Smoking Rooms
.60x .40x

.40x = 10

Therefore .60X=15 Therefore, x = 25



hence % of smoking rooms = 100 - 25 / 100 = 75%


Note: It is also assumed that smoking + Non - Smoking Rooms = 100
Rooms with Queen - sized beds + rooms with king - sized rooms = 100


Hope this really helps for better understanding....

[GMATGuruNY]

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%

Use a group grid to organize the information.
All the values in the group grid have to add up horizontally and vertically:


75% of the guestrooms at the Stagecoach Inn have a queen-sized bed.
10% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds:


Of the non-smoking rooms, 60% have a queen-sized bed.
Thus, of the non-smoking rooms, the 10 with a queen-size bed represent 40% of the total number of non-smoking rooms, implying a total of 25 non-smoking rooms (since 10=.4*25):



Smoking rooms = 75%.

The correct answer is E.

[thinktank08]

Hey!
i was solving this problem the other way round as per the grid, smoking and non smoking rooms to the top and king and queen beds to the left.. however, i got 30 as the total no of smoking rooms. I ve been comparing both our grids for almost 15 mins and i m still not able to figure out how i arrived at the wrong answer despite filling in all values correctly. kindly help

[alexander.vien]

Double-set Matrix! Love it. So much better than a Venn Diagram.

[Tommy Wallach]

Yeah, the problem with Venn diagrams is that there's no distinct place to put a lot of the information. Think of it this way. A Venn diagram with two groups has four distinct places to put things: only in X, only in Y, in the confluence of X&Y, and outside of both circles (which is a weird place to put stuff, visually).

By contrast, the double-set matrix has 9 separate places to put things. So it's just a way more effective way to organize information.

Hope that helps!

-t

[Brent@GMATPrepNow]

As many of the students in this forum already know, the Double Matrix Method can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria for the population of hotel rooms are:
- bed (king or queen)
- smoking (allowed or not allowed)

For more information about this technique and some additional practice questions, check out these 3 BTG articles:

- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent