goyalsau wrote:50% of the aparments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what percent of the apartments with windows have hardwood floors?
a) 40%
b) 10%
c ) 16 2/3 %
d) 50%
e) 83 1/3 %
Whenever we have groups (in this case, apartments with windows and those without) that are being divided into smaller groups (in this case, apartments with hardwood floors and those without), we can use a group grid to organize the data.
Here's what the grid looks like (W = windows, NW = no windows, H = hardwood floors, NH = no hardwood floors):
_______________W______NW_______Total
H:
NH:
total:
In the grid above, every row has to add up to the total, as does every column. Looking at the top row, hardwood floors with windows + hardwood floors with no windows = total hardwood floors. Looking at the left-most column, windows with hardwood floors + windows with no hardwood floors = total windows.
Now let's fill in the data step by step. Whenever we have get 2 entries in a row or a column, we can determine the remaining entry in that row or column.
Let's plug in 100 for the total number of apartments:
_______________W______NW_______Total
H:
NH:
total:_____________________________
100
50% have windows and hardwood floors:
_______________W______NW_______Total
H:_____________
50
NH:
total:______________________________100
40% of the apartments do not have hardwood floors:
_______________W______NW_______Total
H:_____________50______
10__________
60
NH:_______________________________
40
total:______________________________100
25% of the apartments without windows have hardwood floors. Since 10 = .25*40, we must have 40 total apartments with no windows, and the rest of the grid can be completed:
_______________W______NW_______Total
H:_____________50______10_________60
NH:____________
10______
30_________40
total:___________
60______
40_________100
Notice that everything adds up horizontally and vertically. Neat!
Total windows = 60
Windows with hardwood floors = 50
50/60*100 = 83 1/3%
The correct answer is E.
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