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50% of the aparments in a certain building have windows and
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25 Nov 2005, 09:43

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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?

Re: This one will test your skill for Overlapping Sets concept
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16 Sep 2009, 07:57

4

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)

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04 Apr 2013, 15:50

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Tagger wrote:

Still can't get the solution using the Double matrix

Please help !

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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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

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

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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 ?

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

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 _________________

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

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