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

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Manager
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Joined: 29 Nov 2018
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Concentration: Marketing, Strategy
The average of a group of eight friends increases by 4 years when the  [#permalink]

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New post 10 Jan 2019, 12:18
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E

Difficulty:

  55% (hard)

Question Stats:

60% (02:32) correct 40% (01:24) wrong based on 20 sessions

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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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Joined: 20 Sep 2018
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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, 13:46
2
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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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, 20:34
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)

https://www.veritasprep.com/blog/2012/0 ... etic-mean/
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Re: The average of a group of eight friends increases by 4 years when the &nbs [#permalink] 10 Jan 2019, 20:34
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