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John cleaned the windows in his house. After breakfast John cleaned 20

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Arthur9128
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John cleaned the windows in his house. After breakfast John cleaned 20 [#permalink] New post   20 Jan 2021, 05:51
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John cleaned the windows in his house. After breakfast John cleaned 20% of the windows. After lunch he cleaned 30% of the remaining windows. Afterward, John cleaned 50% of the final remaining windows. What percent of the total number of windows were not cleaned?

A. 25%
B. 28%
C. 30%
D. 32%
E. 35%
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B
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Re: John cleaned the windows in his house. After breakfast John cleaned 20 [#permalink] New post   20 Jan 2021, 05:58
After Breakfast:
Cleaned Windows = 20%
Uncleaned windows = 80%

After Lunch:
Cleaned Windows = 30%*80% = 24%
Uncleaned windows = 80%-24% = 56%

After some more time:
Cleaned Windows = 50%*56% = 28%
Uncleaned windows = 56%-28% = 28%

Option B
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Re: John cleaned the windows in his house. After breakfast John cleaned 20 [#permalink] New post   20 Jan 2021, 08:55
John cleaned the windows in his house. After breakfast John cleaned 20% of the windows. After lunch he cleaned 30% of the remaining windows. Afterward, John cleaned 50% of the final remaining windows. What percent of the total number of windows were not cleaned?

1. After breakfast
Cleaned = 20%
Remaining = 80%

2. After lunch
Cleaned = 30% of 80 % = 24%
Remaining = 80% - 24% = 56%

3. Afterward
Cleaned = 50% of 56% = 28%
Remaining = 56% - 28% = 28%

Choice B is the answer.
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Re: John cleaned the windows in his house. After breakfast John cleaned 20 [#permalink] New post   20 Jan 2021, 09:01
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Arthur9128 wrote:
John cleaned the windows in his house. After breakfast John cleaned 20% of the windows. After lunch he cleaned 30% of the remaining windows. Afterward, John cleaned 50% of the final remaining windows. What percent of the total number of windows were not cleaned?

A. 25%
B. 28%
C. 30%
D. 32%
E. 35%

Hello, everyone. A shortcut for these types of questions is to track the percent of what is left at each step and simply multiply everything together:

\(0.8*0.7*0.5=(.56)*0.5=0.28\)

Staggering the information can work just as well, but the above approach may prove faster. Good luck with your studies.

- Andrew
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John cleaned the windows in his house. After breakfast John cleaned 20 [#permalink] New post   21 Jan 2021, 18:42
Took me 7 minutes because of a math error...grueling.

1/5 After breakfast
3/10 x (4/5) = 12/50 = 6/25 after lunch cleaned
1/2 x ( 1 - 1/5 - 6/25) = 14/25 cleaned what's remaining

1 - 14/25 - 7 / 25 = 7/25 left over

7/25 = 0.04 x 7 = 0.28
0.28 x 100 = 28%

Answer is A.
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John cleaned the windows in his house. After breakfast John cleaned 20 [#permalink]
21 Jan 2021, 18:42
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