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vaibhav101: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon May 01, 2017 11:56 pm; Thanked: 4 times

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by vaibhav101 » Wed Aug 01, 2018 9:49 am

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50% of the apartments in a certain building have windows and hardwoods 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 ha e hardwood floors?

A 10%
B 16.66%
C 40%
D 50%
E 83.33%

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Source: Beat The GMAT — Problem Solving | Wed Aug 01, 2018 9:49 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Thu Aug 09, 2018 9:35 am

Let a = total window
b = total of apartment with no window.
Apartment with window and hardwood floor = 50%
$$=\ \frac{50}{100}=\ 0.5$$
$$Apartments\ without\ window\ bat\ have\ hardwood\ floor\ =25\%\ =\ \frac{25}{100\ }=\ 0.25$$

$$Apartments\ without\ hardwood\ floor\ =40\%\ =\ \frac{40}{100\ }=\ 0.4$$
Proportion of apartment with windows = a - b
1 - 0.4 = 0.6
$$\leftDesire\ proprtion\ =\ \frac{\left(Apartment\ with\ windows\ \&\ hardwood\ \right)}{total\ windows}\ \right\cdot\frac{100}{1}$$
$$=\ \frac{0.5}{0.6}\ \cdot\ \frac{100}{1}$$
= 83.33%
Option E is CORRECT.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Aug 10, 2018 5:35 pm

vaibhav101 wrote:50% of the apartments in a certain building have windows and hardwoods 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 ha e hardwood floors?

A 10%
B 16.66%
C 40%
D 50%
E 83.33%

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 = â…š = 83.33% of them have hardwood floors.

Answer: E

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