50% of the aparments in a certain building have windows and

Question

50% of the apartments 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. 10
B. 16 2/3
C. 40
D. 50
E. 83 1/3

A. 10 
B. 16 2/3 
C. 40 
D. 50 
E. 83 1/3

Zarrolou · Accepted Answer

Take a look at the image.

X is the percentage of Non-Window, and we know that 25% of that number has Hardwood => 0.25x is in the cell (NW, H) and 0,75x is, of course, in the (NW, NH) cell.
( 0.25x+0.75x=x ). The tot Hardwood is 60%, and is composed by the first row:  50+0.25x=60  x=40. Ok, we have X, or the tot perc of NonWindows.
Now we know also that  y+40%=100%  and clearly y = 60% => tot perc of W is 60%.This is composed by the cell   and by the cell

And now we have all the data we can have. To answer the question: "what percent of the apartments with windows have hardwood floors?" we must calculate the fraction (apartments with windows and hardwood floors  )/(apartments with windows ) =  \frac{50%}{60%}  =  83 \frac{1}{3}

Hope it's clear

barakhaiev · Answer

E. did it by simple picking numbers and creating a table. check this out.

christoph · Answer

83 1/3...best way is to construct a matrix...

..........h......no h....total
w.......50..................
no w..0,25x............x
total............40......100

fill in...

nakib77 · Answer

yup you need to construct a matrix

 X********| Windows'|No Windows'''| total 
 hardFl****'|50*****''|10*********'|60 
 Not hardFl*|10******|30*********'|40 
 Total*****|60******'|40*********'|100 
 

so percent of the apartments with windows have hardwood floors = 50/60 *100

= 83 1/3

so E is the answer.

katz07 · Answer

E. Is that the correct answer choice. Please post OA.

Here is my working...
a = total windows
b = total of no windows

HW = .5 (given in the problem statement)
(No W,H) = 0.25b
H = 0.6 (given in the problem statement)
No H = 0.4 (deduced as 1 -.06, but this is not needed to solve the problem)

HW + (No W,H) = 0.60
.5+0.25b = 0.60
b = 0.40
Therefore a = 1-b = 1-.40 = 0.60 (proportion of apartments with windows)

Therefore the desired proportion = (HW/a)*100 = (0.5/0.6) * 100 = 83.33% (E).

Goldgoldandgold, could you please confirm the answer.

amit2k9 · Answer

total apartments = 100
with windows and hardwoods = 50
without windows = 50

without windows but having hardwoods = 0.25 *50 = 12.25

12.25 + with windows and hardwoods = 60 
with windows and hardwoods = 47.75

% = 47.75 / 50 > 50%
Hence E.

Amit989 · Answer

------------------

HI Bunuel,

Could you please help here with a quicker way to solve such problems.

I used the Double matrix but it still took me 3 mins or a few secs more. May be bcoz I was trying to be a bit careful/slow trying not to get lost by the question wording.

How can we solve such problems from Sets. Is Matrix the best way ?

Cheers!

chetan2u · Answer

Hi..

In this Q you can get your answer in 10 secs

50% of ALL (that is 100%) apartments have window and hardwood floors..

now we are looking at having BOTH as a % of THOSE having windows..
which will be MORE than 50%. 
ONLY E is left

In form of equation-
 \frac{Both}{W}>\frac{Both}{W+NW}.....\frac{Both}{W}>50% 
 W is house with windows
NW is houses without windows
ALL = W + NW

ScottTargetTestPrep · Answer

We can let the total number of apartments = 100.

So, 50 have windows and hardwood floors.

Since 40 do not have hardwood floors, then 60 do have hardwood floors.

Thus, 60 - 50 = 10 have hardwood floors but no windows.

We are given that 25% of the apartments without windows have hardwood floors and we found the number of such apartments is 10. If 25% of the apartments without windows is 10, the total number of apartments without windows is 10/0.25 = 40. Thus, there are 100 - 40 = 60 apartments that have windows.

Since 50 of them have hardwood floors, 50/60 = ⅚ = 83.33% of them have hardwood floors.

Answer: E

GMATinsight · Answer

Please find the video solution as mentioned

https://www.youtube.com/watch?v=IfuAW9wLFvE

DVR17 · Answer

ARM125 · Answer

I have spent 1 hr on this single question. I had a difficulty of understanding the last sentence of the question "What percent of apartments with windows have hardwood floors".

Best way i can able to find out is assume values. Let's say there are 200 apartments in the building. It is given 50% apartments are with windows and hardwood floors. that is 100. Now we can find out with the help of matrix is  total number of apartments with windows  are 60% i.e 120 apartments.

out of 120 apartments there are 100 apartments with windows and hardwood. We just need to find out what percentage of 120 is 100.

You can follow below calculation if required:

/  = 10/12 =  /12 = 1-  = can be written as 100% - 16.7% = 83.33%

bumpbot · Answer

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50% of the aparments in a certain building have windows and

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50% of the aparments in a certain building have windows and

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615 to 715 in 15 Days (Ria's Strategies)

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