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# If 95% of the residents of Coral Estates live in private homes and 40%

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Math Expert
Joined: 02 Sep 2009
Posts: 58333
If 95% of the residents of Coral Estates live in private homes and 40%  [#permalink]

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01 Mar 2018, 00:18
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15% (low)

Question Stats:

86% (01:00) correct 14% (02:02) wrong based on 53 sessions

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If 95% of the residents of Coral Estates live in private homes and 40% of these live in air-conditioned homes, what percent of the residents of Coral Estates live in air-conditioned homes?

(A) 3%
(B) 3.8%
(C) 30%
(D) 38%
(E) 40%

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Posts: 1140
Re: If 95% of the residents of Coral Estates live in private homes and 40%  [#permalink]

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01 Mar 2018, 00:30
Bunuel wrote:
If 95% of the residents of Coral Estates live in private homes and 40% of these live in air-conditioned homes, what percent of the residents of Coral Estates live in air-conditioned homes?

(A) 3%
(B) 3.8%
(C) 30%
(D) 38%
(E) 40%

Since the calculation is straightforward, we'll just do it.
This is a Precise approach.

The percent of people who live in a home that is both private and air-conditioned is 95%*40%.
Since 10% of 40% is 4\$ then 5% of 40% is 2%. So, 95% of 40% is (100%-5%)*40% = 40% - 2% = 38%

Important note: To answer the question we had to assume that only people in private homes have air-conditioning, otherwise our number could be higher.
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If 95% of the residents of Coral Estates live in private homes and 40%  [#permalink]

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01 Mar 2018, 19:44
Bunuel wrote:
If 95% of the residents of Coral Estates live in private homes and 40% of these live in air-conditioned homes, what percent of the residents of Coral Estates live in air-conditioned homes?

(A) 3%
(B) 3.8%
(C) 30%
(D) 38%
(E) 40%

Assume 100 people. 95% of them live in private homes.

(.95)(100) = 95 people who live in private homes

And 40 percent of these people (the 95) have AC.

$$(\frac{4}{10}*95)=(\frac{2}{5}*95)=19*2= 38$$ people who both live in private homes and have AC

Those 38 are what percent of all residents? There are 100 residents.

$$(\frac{38}{100}*100)=(.38*100) = 38$$ percent

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Re: If 95% of the residents of Coral Estates live in private homes and 40%  [#permalink]

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03 Mar 2018, 00:21
Bunuel wrote:
If 95% of the residents of Coral Estates live in private homes and 40% of these live in air-conditioned homes, what percent of the residents of Coral Estates live in air-conditioned homes?

(A) 3%
(B) 3.8%
(C) 30%
(D) 38%
(E) 40%

IMO D
l will explain through table attached bellow:-
Attachments

Screenshot (81).png [ 112.47 KiB | Viewed 794 times ]

Director
Joined: 27 May 2012
Posts: 902
Re: If 95% of the residents of Coral Estates live in private homes and 40%  [#permalink]

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26 Mar 2018, 06:05
Bunuel wrote:
If 95% of the residents of Coral Estates live in private homes and 40% of these live in air-conditioned homes, what percent of the residents of Coral Estates live in air-conditioned homes?

(A) 3%
(B) 3.8%
(C) 30%
(D) 38%
(E) 40%

Actually the question is asking PVT home AC + Non private home AC = total AC

Attachment:

Table.jpg [ 34.92 KiB | Viewed 712 times ]

We need whats given in the green box.Total AC homes. Both the tables give possible scenarios.
However to get the OA we have to assume that there are no NON PVT homes with AC. That's table 1.

Hope this helps.
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Re: If 95% of the residents of Coral Estates live in private homes and 40%  [#permalink]

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27 Mar 2018, 11:33
Bunuel wrote:
If 95% of the residents of Coral Estates live in private homes and 40% of these live in air-conditioned homes, what percent of the residents of Coral Estates live in air-conditioned homes?

(A) 3%
(B) 3.8%
(C) 30%
(D) 38%
(E) 40%

We can let the total number of people = 100.

So 95 people have private homes and 95 x 0.4 = 38 people live in air-conditioned homes.

So 38% live in air-conditioned homes.

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Re: If 95% of the residents of Coral Estates live in private homes and 40%  [#permalink]

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27 Mar 2018, 11:39
Bunuel wrote:
If 95% of the residents of Coral Estates live in private homes and 40% of these live in air-conditioned homes, what percent of the residents of Coral Estates live in air-conditioned homes?

(A) 3%
(B) 3.8%
(C) 30%
(D) 38%
(E) 40%

40% of 95 is just less than 40% of 100 only option is D-38%

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Re: If 95% of the residents of Coral Estates live in private homes and 40%   [#permalink] 27 Mar 2018, 11:39
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