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Among a population of 30,000 people, 45 percent live within 10 miles

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Among a population of 30,000 people, 45 percent live within 10 miles [#permalink]

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New post 03 Oct 2017, 11:12
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Question Stats:

76% (02:23) correct 24% (01:44) wrong based on 42 sessions

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Among a population of 30,000 people, 45 percent live within 10 miles of their workplace, 78 percent live inside the city limits of Town T, and 33 percent live both within 10 miles of their workplace and inside the city limits of Town T. If 1 person is to be randomly selected from the 30,000 people, what is the probability that the person lives within 10 miles of their workplace but NOT inside the city limits of Town T?

(A) 3/25
(B) 3/10
(C) 33/100
(D) 12/25
(E) 9/20
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Oct 2017, 11:17, edited 1 time in total.
Edited the options.

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Re: Among a population of 30,000 people, 45 percent live within 10 miles [#permalink]

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New post 03 Oct 2017, 11:26
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Turkish wrote:
Among a population of 30,000 people, 45 percent live within 10 miles of their workplace, 78 percent live inside the city limits of Town T, and 33 percent live both within 10 miles of their workplace and inside the city limits of Town T. If 1 person is to be randomly selected from the 30,000 people, what is the probability that the person lives within 10 miles of their workplace but NOT inside the city limits of Town T?

(A) 3/25
(B) 3/10
(C) 33/100
(D) 12/25
(E) 9/20


The number of people who live within 10 miles of their workplace but NOT inside the city limits of Town T = {Within 10 miles} - {Both} = 0.45*30,000 - 0.33*30,000 = 3,600

P = 3,600/30,000 = 3/25.

Answer: A.
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Re: Among a population of 30,000 people, 45 percent live within 10 miles [#permalink]

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New post 03 Oct 2017, 22:25
Turkish wrote:
Among a population of 30,000 people, 45 percent live within 10 miles of their workplace, 78 percent live inside the city limits of Town T, and 33 percent live both within 10 miles of their workplace and inside the city limits of Town T. If 1 person is to be randomly selected from the 30,000 people, what is the probability that the person lives within 10 miles of their workplace but NOT inside the city limits of Town T?

(A) 3/25
(B) 3/10
(C) 33/100
(D) 12/25
(E) 9/20



We can solve this question just using the %, as all the values are given in % form.

45% live within 10 miles of their workplace
78% live inside the city limits of Town T
33% live both within 10 miles of their workplace and inside the city limits of Town T

the % person lives within 10 miles of their workplace but NOT inside the city limits of Town T= [% of People living in 10 mile radius of work place] -[% of People living in both winthin 10 mile radius and inside city limit]
=45% - 33% = 12%

Probability of % person lives within 10 miles of their workplace but NOT inside the city limits of Town T = 12/100 = 3/25 [12% out of 100%]

Answer: A

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Re: Among a population of 30,000 people, 45 percent live within 10 miles [#permalink]

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New post 25 Oct 2017, 15:44
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Turkish wrote:
Among a population of 30,000 people, 45 percent live within 10 miles of their workplace, 78 percent live inside the city limits of Town T, and 33 percent live both within 10 miles of their workplace and inside the city limits of Town T. If 1 person is to be randomly selected from the 30,000 people, what is the probability that the person lives within 10 miles of their workplace but NOT inside the city limits of Town T?

(A) 3/25
(B) 3/10
(C) 33/100
(D) 12/25
(E) 9/20


30,000 people
live within 10 miles: 30000(0.45) = 13,500
Live in city limits: 30000(0.78) = 23,400
Both: 30,000(0.33) = 9,900

People who live within 10 miles, but not in city limits 13,500 - 9,900 = 3,600

Probability of people who live within 10 miles, but not in city limits: 3,600/30,000 = 3/25

You do not need to really solve for the amount of people who live in city limits (78% of 30,000), I just did.

Kudos [?]: 6 [0], given: 73

Re: Among a population of 30,000 people, 45 percent live within 10 miles   [#permalink] 25 Oct 2017, 15:44
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