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The table above shows the age of 6 friends. The average age of the six
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03 Aug 2023, 01:23
03 Aug 2023, 01:23
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The table above shows the age of 6 friends. The average age of the six friends is 16 years. If no person is less than 14 or greater than 20 years of age, what is the maximum average age of the 4 eldest people in the group?
A. 16
B. 16.5
C. 16.75
D. 17
E. 17.5
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Re: The table above shows the age of 6 friends. The average age of the six
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16 Sep 2023, 23:14
16 Sep 2023, 23:14
Expert Reply
OE
We are given that in a sequence of the age of 6 friends, the average age is 16 years.
No person is less than 14 or greater than 20 years.
We need to find the maximum average age of the 4 eldest people in the group.
Since, average age of A, B, C,D, E and F is 16 years,
Sum of their ages = Average × Number of people
= 16 × 6
= 96 years
4 + 15 + 𝑥 + 18 + 19 + 𝑦 = 96
𝑥 + 𝑦 = 30
We want to find the maximum average age of four eldest people.
To get the maximum average age, we should get the maximum sum of the age of
four eldest people in the group.
We know that 𝑥 + 𝑦 = 30.
If 𝑥 = 15, 𝑦 = 15 then the maximum age we are getting is 19, 18, 15, 15 which is
not giving us maximum sum.
So instead, we can take 𝑥 = 16 then 𝑦 = 14 and the maximum age we are getting
are: 19, 18, 16, 15 which is more than the previous case.
If we take 𝑥 = 17 then we are getting 𝑦 = 13 which is not applicable since no one
is less than 14.
Hence, we cannot consider 𝑥 more than 16.
Now eldest four have got ages as 15, 16, 18 and 19 years.
Average=15+16+18+19/4=17
D is the answer
We are given that in a sequence of the age of 6 friends, the average age is 16 years.
No person is less than 14 or greater than 20 years.
We need to find the maximum average age of the 4 eldest people in the group.
Since, average age of A, B, C,D, E and F is 16 years,
Sum of their ages = Average × Number of people
= 16 × 6
= 96 years
4 + 15 + 𝑥 + 18 + 19 + 𝑦 = 96
𝑥 + 𝑦 = 30
We want to find the maximum average age of four eldest people.
To get the maximum average age, we should get the maximum sum of the age of
four eldest people in the group.
We know that 𝑥 + 𝑦 = 30.
If 𝑥 = 15, 𝑦 = 15 then the maximum age we are getting is 19, 18, 15, 15 which is
not giving us maximum sum.
So instead, we can take 𝑥 = 16 then 𝑦 = 14 and the maximum age we are getting
are: 19, 18, 16, 15 which is more than the previous case.
If we take 𝑥 = 17 then we are getting 𝑦 = 13 which is not applicable since no one
is less than 14.
Hence, we cannot consider 𝑥 more than 16.
Now eldest four have got ages as 15, 16, 18 and 19 years.
Average=15+16+18+19/4=17
D is the answer
gmatclubot
Re: The table above shows the age of 6 friends. The average age of the six [#permalink]
16 Sep 2023, 23:14
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