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The average of a group of eight friends increases by 4 years when the

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New post 10 Jan 2019, 13:18
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The average of a group of eight friends increases by 4 years when the youngest of them is not considered and decreases by 3 years when the oldest of them is not considered. Find the difference between the ages of oldest and the youngest of them.

A 49 yrs
B 52 yrs
C 55 yrs
D 56 yrs
E 58 yrs
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Re: The average of a group of eight friends increases by 4 years when the  [#permalink]

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New post 10 Jan 2019, 14:46
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Let the ages from Youngest to the Oldest be Al... A8 Given:
Al+...+ A8= 8x
A2+.. +A8= 7(x+4) and
Al+...+ A7= 7 (x-3)
subtracting eqn 3 from 2 we have:
A8 - A1=7( x+4)-7( x-3)
⇒ A8- Al=49

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New post 10 Jan 2019, 21:34
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cfc198 wrote:
The average of a group of eight friends increases by 4 years when the youngest of them is not considered and decreases by 3 years when the oldest of them is not considered. Find the difference between the ages of oldest and the youngest of them.

A 49 yrs
B 52 yrs
C 55 yrs
D 56 yrs
E 58 yrs


When 7 friends are considered such that youngest is not considered, the avg is A + 4
When 7 friends are considered such that oldest is not considered, the avg is A - 3

A difference of 7 is created in the avg because the oldest friend has 7 more for each of the 7 friends than what the youngest friend has.
So the oldest has 7*7 = 49 more than the youngest.

Answer (A)

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Re: The average of a group of eight friends increases by 4 years when the  [#permalink]

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New post 30 Mar 2019, 00:43
My approach to this question was

Assume average age of 50 for 8 persons. 1.Average age becomes 54 for 7 persons hence youngest age must be 22 (using 50*8- 54*7) and
2. similarly average age becomes 47 for 7 persons so oldest age is 71
3 difference is 49

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Re: The average of a group of eight friends increases by 4 years when the  [#permalink]

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New post 30 Mar 2019, 01:19
1
cfc198 wrote:
The average of a group of eight friends increases by 4 years when the youngest of them is not considered and decreases by 3 years when the oldest of them is not considered. Find the difference between the ages of oldest and the youngest of them.

A 49 yrs
B 52 yrs
C 55 yrs
D 56 yrs
E 58 yrs


sum of 7 / 7 = x+4
sum of 7 = 7x+28 ;; youngest

oldest is removed
sum of 7 = (x-3)*7 ; 7x-21
difference in age
7x-21-7x-28 . =- 49
age cannot be -ve ; 49
IMO A
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Re: The average of a group of eight friends increases by 4 years when the   [#permalink] 30 Mar 2019, 01:19
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