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If the average (arithmetic mean) annual income for a group of people

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If the average (arithmetic mean) annual income for a group of people  [#permalink]

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New post 25 Jan 2018, 23:54
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If the average (arithmetic mean) annual income for a group of people is x, where x >0, and the annual income of one of the members of the group, Joe, increases by 25%, by what percent does the average income of the whole group increase?

(1) There are 8 people in the group.
(2) The total initial income of the group is 9 times Joe's initial income.

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Re: If the average (arithmetic mean) annual income for a group of people  [#permalink]

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New post 26 Jan 2018, 00:12
IMO B

1) Initial total income = 8x, New total = 8x - Joe's previous income + Joe's new income. No idea about what was Joe's previous income or even how it was related with group's income to estimate the change in total income, therefore Not Sufficient.

2) Joe's initial income = a, Group's initial income=9a, total income=10a
Joe's new income = 1.25a, Group's new income = 9+1.25a=10.25a
Therefore % change in average=% change in total income= 2.5%, Sufficient.
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Re: If the average (arithmetic mean) annual income for a group of people  [#permalink]

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New post 26 Jan 2018, 00:45
urvashis09 wrote:
IMO B

1) Initial total income = 8x, New total = 8x - Joe's previous income + Joe's new income. No idea about what was Joe's previous income or even how it was related with group's income to estimate the change in total income, therefore Not Sufficient.

2) Joe's initial income = a, Group's initial income=9a, total income=10a
Joe's new income = 1.25a, Group's new income = 9+1.25a=10.25a
Therefore % change in average=% change in total income= 2.5%, Sufficient.



Hi

I also think the answer is B. Similar logic as yours. But in second statement, I think total income will be 9a only, and not 10a. After increase in Joe's income, group's total income will be = 9.25a. % increase = 0.25/9 * 100.
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Re: If the average (arithmetic mean) annual income for a group of people  [#permalink]

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New post 26 Jan 2018, 00:57
Option B

Let Joe's initial income be J
Hence, new income will be 1.25J

Let total income of others in the group be R and the no. of members be m.

Hence, old average: (J + R)/m
New average: (1.25J + R)/m

Percentage difference: [(1.25J + R)/m] - [(J + R)/m] / (J + R)/m

= 0.25J / J + R

Statement one is not needed to fulfil this.
Statement two tells you that R = 9J.
Plug that into our equation: 0.25J / 9J + J = 2.5% increase
SUFFICIENT



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Re: If the average (arithmetic mean) annual income for a group of people  [#permalink]

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New post 26 Jan 2018, 01:40
amanvermagmat wrote:
urvashis09 wrote:
IMO B

1) Initial total income = 8x, New total = 8x - Joe's previous income + Joe's new income. No idea about what was Joe's previous income or even how it was related with group's income to estimate the change in total income, therefore Not Sufficient.

2) Joe's initial income = a, Group's initial income=9a, total income=10a
Joe's new income = 1.25a, Group's new income = 9+1.25a=10.25a
Therefore % change in average=% change in total income= 2.5%, Sufficient.



Hi

I also think the answer is B. Similar logic as yours. But in second statement, I think total income will be 9a only, and not 10a. After increase in Joe's income, group's total income will be = 9.25a. % increase = 0.25/9 * 100.



Yes, group does include Joe too. Agreed! Thanks again!
Re: If the average (arithmetic mean) annual income for a group of people &nbs [#permalink] 26 Jan 2018, 01:40
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