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

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GMAT Club Legend
Joined: 29 Jan 2005
Posts: 4068
50% of the aparments in a certain building have windows and  [#permalink]

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25 Nov 2005, 09:43
2
29
00:00

Difficulty:

65% (hard)

Question Stats:

68% (02:51) correct 32% (02:56) wrong based on 588 sessions

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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
Intern
Joined: 12 Sep 2009
Posts: 3
Re: This one will test your skill for Overlapping Sets concept  [#permalink]

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16 Sep 2009, 07:57
4

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).

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Re: This one will test your skill for Overlapping Sets concept  [#permalink]

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16 Sep 2009, 10:32
4
E. did it by simple picking numbers and creating a table. check this out.
Attachments

solution.xls [7 KiB]

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

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04 Apr 2013, 15:50
2
Tagger wrote:
Still can't get the solution using the Double matrix

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 [Window, Hardwood (50%)] and by the cell [Window, NonHardwood (that must be 10% since 50%+10%=60%)]

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 [W,H])/(apartments with windows[W]) = $$\frac{50%}{60%}$$ = $$83 \frac{1}{3}$$

Hope it's clear
Attachments

matrix.png [ 2.63 KiB | Viewed 9804 times ]

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25 Nov 2005, 10:04
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...
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25 Nov 2005, 15:38
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

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Re: This one will test your skill for Overlapping Sets concept  [#permalink]

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02 May 2011, 02:07
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]

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29 Oct 2016, 07:32
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,

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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Joined: 02 Aug 2009
Posts: 8142
Re: 50% of the aparments in a certain building have windows and  [#permalink]

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07 Sep 2017, 07:43
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..

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]

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10 Aug 2018, 18:42
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.

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

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08 Oct 2018, 22:38
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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50% of the aparments in a certain building have windows and   [#permalink] 08 Oct 2018, 22:38
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