Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to pre-think assumptions and solve the most challenging questions in less than 2 minutes.

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

Show Tags

25 Nov 2005, 09:43

2

29

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

69% (02:51) correct 31% (02:55) wrong based on 584 sessions

HideShow timer Statistics

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?

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

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

Show Tags

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)

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

Show Tags

04 Apr 2013, 15:50

2

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 9715 times ]

_________________

It is beyond a doubt that all our knowledge that begins with experience.

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

Show Tags

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,

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
[#permalink]

Show Tags

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
[#permalink]

Show Tags

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
[#permalink]

Show Tags

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

_________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html