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# A total of 9 women and 12 men reside in the 21 apartments that are in

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Math Expert
Joined: 02 Sep 2009
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A total of 9 women and 12 men reside in the 21 apartments that are in  [#permalink]

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15 Dec 2014, 09:26
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93% (01:04) correct 7% (01:07) wrong based on 72 sessions

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Tough and Tricky questions: Word Problems.

A total of 9 women and 12 men reside in the 21 apartments that are in a certain apartment building, one person to each apartment. If a poll taker is to select one of the apartments at random, what is the probability that the resident of the apartment selected will be a woman who is a student?

(1) Of the women, 4 are students.
(2) Of the women, 5 are not students.

Kudos for a correct solution.

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Re: A total of 9 women and 12 men reside in the 21 apartments that are in  [#permalink]

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15 Dec 2014, 10:41
statement 1: sufficient
If 4 of the women are students, the chance of randomly selecting 1 among the 21 apartments is 4/21

statement 2: sufficient
If 5 of the women are not students, then 9-5=4 of the women are students. Same as above.

Intern
Joined: 13 Sep 2015
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Re: A total of 9 women and 12 men reside in the 21 apartments that are in  [#permalink]

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12 Mar 2016, 10:34
I thought that the correct answer is A.
The statement 2 claims that: of the women, 5 are not students. But, it does no mean that the other 4 are students. They could be workers, teachers, etc. if the other 4 are students, the probability is 4 / 21. If not, we do not know. So, statement 2 is not sufficient....
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Re: A total of 9 women and 12 men reside in the 21 apartments that are in  [#permalink]

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31 Mar 2018, 06:44
Quote:
A total of 9 women and 12 men reside in the 21 apartments that are in a certain apartment building, one person to each apartment. If a poll taker is to select one of the apartments at random, what is the probability that the resident of the apartment selected will be a woman who is a student?

(1) Of the women, 4 are students.
(2) Of the women, 5 are not students.

chetan2u
In Statement 2, How can we be so sure that the remaining 4 women are students?
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Re: A total of 9 women and 12 men reside in the 21 apartments that are in  [#permalink]

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31 Mar 2018, 11:01
1
itisSheldon wrote:
Quote:
A total of 9 women and 12 men reside in the 21 apartments that are in a certain apartment building, one person to each apartment. If a poll taker is to select one of the apartments at random, what is the probability that the resident of the apartment selected will be a woman who is a student?

(1) Of the women, 4 are students.
(2) Of the women, 5 are not students.

chetan2u
In Statement 2, How can we be so sure that the remaining 4 women are students?

Hi...
When it comes to being a student, there are ONLY 2 possiblities - student or not a student.
So if 5 women are not students, the remaining 4 are of the other category- students.
May be within them out have people from US, India, France, UK etc but the number of women who are students will remain 9-5=4
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A total of 9 women and 12 men reside in the 21 apartments that are in  [#permalink]

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01 Apr 2018, 21:55
Bunuel wrote:

Tough and Tricky questions: Word Problems.

A total of 9 women and 12 men reside in the 21 apartments that are in a certain apartment building, one person to each apartment. If a poll taker is to select one of the apartments at random, what is the probability that the resident of the apartment selected will be a woman who is a student?

(1) Of the women, 4 are students.
(2) Of the women, 5 are not students.

Kudos for a correct solution.

Total Residents =21
No. of Women = 9
Let X be the no of women who are students.

Probability to select Woman P (Woman) = $$\frac{9}{12}$$
Probability of getting a Women who is student = $$\frac{P(Women)*X}{9}$$
P(WomanStudent) = $$\frac{9}{21}*\frac{X}{9}$$
P(WomanStudent) = X/21

Now X we can find from both statement 1 and 2 seperately

Therefore Option D
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Re: A total of 9 women and 12 men reside in the 21 apartments that are in  [#permalink]

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02 Aug 2019, 05:29
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Re: A total of 9 women and 12 men reside in the 21 apartments that are in   [#permalink] 02 Aug 2019, 05:29
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