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# In a village of 2,500 people, 800 people are over 70 years old and 850

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Math Expert
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In a village of 2,500 people, 800 people are over 70 years old and 850 [#permalink]

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06 Apr 2016, 06:58
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In a village of 2,500 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?

A. 221/250
B. 199/250
C. 33/50
D. 8/25
E. 51/250
[Reveal] Spoiler: OA

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Manager
Joined: 09 Jul 2013
Posts: 110
Re: In a village of 2,500 people, 800 people are over 70 years old and 850 [#permalink]

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06 Apr 2016, 09:33
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To solve this we would need to know the number of people who are less than 70 years old, the number of males, and the number of males who are less than 70 years old.

Overlapping sets: quantity of A or B = A + B - (A∩B) = quantity of A + quantity of B - (intersection of A and B)

Number of males = 2500-850 = 1650
Number of people below 70 years old = 2500-800 = 1700
Number of males below 70 years old = 1700-(850*0.4) = 1360

Total number of people who are male OR below 70 = 1650 + 1700 - 1360 = 1990

Probability of male or below 70 = 1990/2500 = 199/250

Answer: B
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Dave de Koos
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Posts: 5713
In a village of 2,500 people, 800 people are over 70 years old and 850 [#permalink]

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06 Apr 2016, 09:57
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Bunuel wrote:
In a village of 2,500 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?

A. 221/250
B. 199/250
C. 33/50
D. 8/25
E. 51/250

Hi,

we can get the probability of answering this correct from $$\frac{1}{5}to \frac{1}{2}$$within 10 secs by realizing that --

1) Choices

prob of choosing a<70 years old = $$\frac{(2500-800)}{2500}= \frac{170}{250}$$..
we have to add male>70 year old to it so $$P> \frac{170}{250}$$
you can eliminate C, D and E ..

NOW we have to add male>70 year old to it ..
60 % F, which is 850 are >70yr old, so male >70 will be less than 50% of Total 800 = 400..
so our answer $$< 1700+400 = 2100..$$
so$$P<\frac{2100}{2500}$$
ONLY B is left
B

2) Proper Method

lets solve further
F=850 ..
60% of 850 = 510 are >70 year old..
Total >70 yr old = 800.. so M in that =800-510 = 290..
Also total<70 yr= 2500-800=1700..
the probability that a person chosen at random is either a male or younger than 70 years old=$$\frac{(1700+290)}{2500}= \frac{199}{250}$$
B

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Manager
Joined: 17 Aug 2015
Posts: 105
Re: In a village of 2,500 people, 800 people are over 70 years old and 850 [#permalink]

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04 Jul 2016, 21:15
after solving this problem I learnt two things:
1) Reading the question well enough tells us what to solve for and avoids taking longer routes.
2) If we adopt an accounting approach via something like a double matrix here, it will become more challenging to solve this problem.

The question gives info on Females and population older than 70 years, but asks about a probability of males or younger. Well some arithmetic and probability we need to do.

P(male or <70 yrs) = Prob(male)+Prob(<70)-Prob(male and <70).
let us compute our sample space
n(male) = 2500-850 = 2550-900=1650.
Notice that second part is really number of female and <70 yrs = > 2/5*850= 340.
n of event space = 1650+340 = 1990.
prob = n of event space / number of entire population = 1990/2500 =>199/250.
Intern
Joined: 11 Oct 2017
Posts: 22
Re: In a village of 2,500 people, 800 people are over 70 years old and 850 [#permalink]

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25 Oct 2017, 11:36
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Bunuel wrote:
In a village of 2,500 people, 800 people are over 70 years old and 850 people are female. It is known that 40 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?

A. 221/250
B. 199/250
C. 33/50
D. 8/25
E. 51/250

2500 people

800 over 70

850 female

40% female younger than 70 = 850(0.4) = 340

850 - 340 = 510 greater than 70 for female

Males = 2500 - 850 = 1650

If 800 are greater than 70 and 510 females are greater than 70, then 800 - 510 = 290 males are greater than 70 years old.

1650 - 290 = 1360 males younger than 70

probability that a person chosen at random is either a male or younger than 70 years old:

(total males, which includes less than 70 years + females less than 70) = 1650 + 340 = 1990

1990/2500 = 199/250 B

or (males less than 70 + females less than 70 + males over 70) = 1360+340+290 = 1990

1990/2500 = 199/250 B
Re: In a village of 2,500 people, 800 people are over 70 years old and 850   [#permalink] 25 Oct 2017, 11:36
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# In a village of 2,500 people, 800 people are over 70 years old and 850

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