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In a family of four people, none of the people have the same
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14 May 2020, 14:15

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Question Stats:

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

Indicate four such ages.

❑ 2

❑ 3

❑ 5

❑ 7

❑ 11

❑ 41

❑ 43

❑ 47

ShowHide Answer

Official Answer

B,C,F,G

Re: In a family of four people, none of the people have the same
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08 Oct 2020, 04:34

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For the first range we can take: 2,3,5,7,11

For the second range we can take: 41,43,47

Now we find the min and max avg:

min = (2+3+41+43)/4 = 22.5

max = (7+11+43+47)/4 = 29.5

The only two prime numbers with the range 22.5 and 29.5 is 23 and 29.

23*4 = 92

29*4 = 116

No Combination of numbers add up to 116 but 3,5,41,43 add up to 92.

For the second range we can take: 41,43,47

Now we find the min and max avg:

min = (2+3+41+43)/4 = 22.5

max = (7+11+43+47)/4 = 29.5

The only two prime numbers with the range 22.5 and 29.5 is 23 and 29.

23*4 = 92

29*4 = 116

No Combination of numbers add up to 116 but 3,5,41,43 add up to 92.

Re: In a family of four people, none of the people have the same
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15 May 2020, 13:52

5

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

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

Re: In a family of four people, none of the people have the same
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20 May 2020, 06:47

1

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

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?

Re: In a family of four people, none of the people have the same
[#permalink]
20 May 2020, 08:00

1

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.

Re: In a family of four people, none of the people have the same
[#permalink]
24 Jun 2020, 23:20

1

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

Re: In a family of four people, none of the people have the same
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22 Oct 2021, 07:59

avg is 21.5?

Re: In a family of four people, none of the people have the same
[#permalink]
19 Jun 2022, 11:03

2

I used the solution that was already provided here, but I added some changes.

We have two sets.

Set A --- 2, 3, 5, 11

Set B --- 41, 43, 47

We need to choose two numbers from each set.

Also the sum of these four numbers should be even. If we take four numbers and sum them, we have three odd numbers, and therefore, the fourth number must be also odd to make the case be even.

odd+odd+odd+[must be odd to make the sum be even].

So we can remove 2 from set A.

Set A --- 3, 5, 11

Set B --- 41, 43, 47

Now we want to find the smallest and the largest possible average:

Smallest: (3+5+41+43)\4 = 23

Largest: (5+11+43+47)\4= 26.5

So we need to find all prime numbers between 23 and 26.5.

23 is the the prime number, and we know the is was created by 3,5,41,43, so these four numbers are the answer.

We have two sets.

Set A --- 2, 3, 5, 11

Set B --- 41, 43, 47

We need to choose two numbers from each set.

Also the sum of these four numbers should be even. If we take four numbers and sum them, we have three odd numbers, and therefore, the fourth number must be also odd to make the case be even.

odd+odd+odd+[must be odd to make the sum be even].

So we can remove 2 from set A.

Set A --- 3, 5, 11

Set B --- 41, 43, 47

Now we want to find the smallest and the largest possible average:

Smallest: (3+5+41+43)\4 = 23

Largest: (5+11+43+47)\4= 26.5

So we need to find all prime numbers between 23 and 26.5.

23 is the the prime number, and we know the is was created by 3,5,41,43, so these four numbers are the answer.

Re: In a family of four people, none of the people have the same
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11 Feb 2024, 11:51

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