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

Question

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%

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

akhilbajaj · Accepted Answer

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

Answer E

WoundedTiger · Answer

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

gauravsoni · Answer

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.

Bunuel · 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.

unceldolan · Answer

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.

PareshGmat · Answer

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

dishamaitra · Answer

Information about no of queen & king size beds is of no use for the solution.

BillyZ · Answer

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 queen-sized bed, while 25 have a king-sized bed.

Of the non-smoking rooms (let's call this unknown n), 60% or .6n have queen-sized beds.

10 rooms are non-smoking with king-sized 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 double-set 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.

KrishnakumarKA1 · Answer

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 = 100-x
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%

bumpbot · Answer

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

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