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In a family of four people, none of the people have the same

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In a family of four people, none of the people have the same [#permalink] New post 14 May 2020, 14:15
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In a family of four people, none of the people have the same age, but all are a prime number of years old. Two of the people are less than 12 years old, and the other two people are between 40 and 52 years old. If the average of their four ages is also a prime number, what are the ages of the family members?

Indicate four such ages.

❑ 2

❑ 3

❑ 5

❑ 7

❑ 11

❑ 41

❑ 43

❑ 47
[Reveal] Spoiler: OA

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Re: In a family of four people, none of the people have the same [#permalink] New post 15 May 2020, 13:52
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Two of the people are less than 12 years old, possible age: 2, 3, 5, and 7
the other two people are between 40 and 52 years old, possible age: 41, 43, 47
If the average of their four ages is also a prime number,
min possible avg of ages = (2+2+41+41)/4 = 86/4 = 21.5
max possible avg of ages = (7+7+47+47)/4 = 108/4 = 27
as mentioned, none of the people has the same age and the average of their four ages is also a prime number, it means the avg is in between 21.5 and 27 and a prime no. i.e. 23
the sum of all four ages = 4*23 = 92
only 3, 5, 41 and 43 can give a sum 92
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Re: In a family of four people, none of the people have the same [#permalink] New post 20 May 2020, 06:47
vndnjn wrote:
Two of the people are less than 12 years old, possible age: 2, 3, 5, and 7
the other two people are between 40 and 52 years old, possible age: 41, 43, 47
If the average of their four ages is also a prime number,
min possible avg of ages = (2+2+41+41)/4 = 86/4 = 21.5
max possible avg of ages = (7+7+47+47)/4 = 108/4 = 27
as mentioned, none of the people has the same age and the average of their four ages is also a prime number, it means the avg is in between 21.5 and 27 and a prime no. i.e. 23
the sum of all four ages = 4*23 = 92
only 3, 5, 41 and 43 can give a sum 92



Why you have not taken 11 as max. possible avg age?
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Re: In a family of four people, none of the people have the same [#permalink] New post 20 May 2020, 08:00
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kanny wrote:
Why you have not taken 11 as max. possible avg age?


If I understood your que correctly; We have to select two no from 2, 3, 5, and 7 and two no from 41, 43, 47.
With any combination, we can not have 11 as vag value of four of these no. The min possible avg is 21.5.
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Re: In a family of four people, none of the people have the same [#permalink] New post 24 Jun 2020, 23:20
vndnjn wrote:
kanny wrote:
Why you have not taken 11 as max. possible avg age?


If I understood your que correctly; We have to select two no from 2, 3, 5, and 7 and two no from 41, 43, 47.
With any combination, we can not have 11 as vag value of four of these no. The min possible avg is 21.5.


I think he meant, 11 is also less than 12 so this is also the possible age
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Re: In a family of four people, none of the people have the same   [#permalink] 24 Jun 2020, 23:20
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