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[#permalink]
1
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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.[/u]
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Re: This one will test your skill for Overlapping Sets concept [#permalink]
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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.
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Re: This one will test your skill for Overlapping Sets concept [#permalink]
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E. did it by simple picking numbers and creating a table. check this out.
Attachments

solution.xls [7 KiB]
Downloaded 1205 times

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Re: This one will test your skill for Overlapping Sets concept [#permalink]
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.
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50% of the aparments in a certain building have windows and [#permalink]
GMATT73 wrote:
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




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

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!
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Re: 50% of the aparments in a certain building have windows and [#permalink]
Expert Reply
GMATT73 wrote:
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


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
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Re: 50% of the aparments in a certain building have windows and [#permalink]
Expert Reply
GMATT73 wrote:
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


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
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50% of the aparments in a certain building have windows and [#permalink]
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Expert Reply
GMATT73 wrote:
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


Please find the video solution as mentioned




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Re: 50% of the aparments in a certain building have windows and [#permalink]
GMATT73 wrote:
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

Attachments

2020-02-03 (1).png
2020-02-03 (1).png [ 7.23 KiB | Viewed 9375 times ]

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Re: 50% of the aparments in a certain building have windows and [#permalink]
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Kudos
Not all apartments have 50% windows some are having ventilation also.
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Re: 50% of the aparments in a certain building have windows and [#permalink]
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