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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
14 May 2020, 14:15
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Question Stats:
53% (02:42) correct
46% (02:43) wrong based on 139 sessions
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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
Indicate four such ages.
❑ 2
❑ 3
❑ 5
❑ 7
❑ 11
❑ 41
❑ 43
❑ 47
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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
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.
General Discussion
Re: In a family of four people, none of the people have the same
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15 May 2020, 13:52
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
