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

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Current Student
Joined: 29 Jan 2005
Posts: 5218
50% of the aparments in a certain building have windows and [#permalink]

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25 Nov 2005, 09:43
1
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15
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Difficulty:

65% (hard)

Question Stats:

63% (03:28) correct 37% (02:11) wrong based on 415 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
[Reveal] Spoiler: OA
VP
Joined: 30 Sep 2004
Posts: 1480
Location: Germany

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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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Joined: 28 May 2005
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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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Intern
Joined: 12 Sep 2009
Posts: 4
Re: This one will test your skill for Overlapping Sets concept [#permalink]

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16 Sep 2009, 07:57
3
KUDOS

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).

Manager
Joined: 10 Jul 2009
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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
2
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E. did it by simple picking numbers and creating a table. check this out.
Attachments

solution.xls [7 KiB]

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

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04 Apr 2013, 15:50
1
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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 5996 times ]

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

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22 Oct 2013, 00:00
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Re: 50% of the aparments in a certain building have windows and [#permalink]

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27 Apr 2015, 04:22
Hello from the GMAT Club BumpBot!

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

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31 Jul 2016, 23:15
Hello from the GMAT Club BumpBot!

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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!
50% of the aparments in a certain building have windows and   [#permalink] 29 Oct 2016, 07:32
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