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# If the total income of a state increases by 50% and the population of

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Manager
Joined: 29 May 2008
Posts: 111

Kudos [?]: 131 [0], given: 0

If the total income of a state increases by 50% and the population of [#permalink]

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07 Sep 2009, 05:50
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Difficulty:

15% (low)

Question Stats:

83% (01:05) correct 17% (01:21) wrong based on 115 sessions

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If the total income of a state increases by 50% and the population of the state increases by 20%, What is the percent change in per capita income for the state?

A) A net increase of 40%
B) A net increase of 30%
C) A net increase of 25%
D) A net increase of 20%
E) A net decrease of 20%
[Reveal] Spoiler: OA

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Manager
Joined: 25 Aug 2009
Posts: 174

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Re: If the total income of a state increases by 50% and the population of [#permalink]

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07 Sep 2009, 09:23
Let I is the total income and P is the totla population..

=> per/capita C (income per person)= $$\frac{I}{P}$$

$$Now, C' = \frac{3I}{2} * \frac{5}{6P}$$

=> C' = $$\frac{5I}{4P}$$

change or increase = $$\frac{(C' - C}{C)} * 100$$
= 25 % increase

ans is C

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Director
Joined: 01 Apr 2008
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Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: If the total income of a state increases by 50% and the population of [#permalink]

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07 Sep 2009, 09:27
Per capita income = income per person
Let P be the total poplulation and I be the total income.
PCI = I/P

After the increase PCI = 1.5I/1.4P = (5/4) * (I/P) = 1.25*(I/P) so PCI has increased by 25%.
C

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Manager
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Re: If the total income of a state increases by 50% and the population of [#permalink]

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08 Sep 2009, 08:54
2
KUDOS
What those OA mean?

The right answer is C

I did it this way

suposse you have, lets say $200 income total and 10 people So you have$20 per capita income

then you now that 50% is added to the $200 so you get$300
for ppl we get an increase of 25% meaning 12 people

and now just divide it 300/12 = 25
25 is 125% of 20

so 25% increase!

is this approach correct?

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EMPOWERgmat Instructor
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Re: If the total income of a state increases by 50% and the population of [#permalink]

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19 Feb 2015, 13:15
3
KUDOS
Expert's post
Hi All,

These types of percent-based questions are often perfect for TESTing VALUES (and the number 100 tends to be a great number to TEST).

We're told that the total income of a state increases by 50% and the total population increases by 20%

To start:
Total Income = $100 Total Population = 100 people$100/100 = $1 per person After the increase: New Total Income =$150
New Total Population = $120$150/120 = $5/4 per person The question asks for the percent increase in per capita income, which means that we need to use the Percentage Change Formula: Percent Change = (New - Old)/Old New = 5/4 Old = 1 (5/4 - 1)/1 = (1/4)/1 = 1/4 = 25% increase Final Answer: [Reveal] Spoiler: C GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If the total income of a state increases by 50% and the population of [#permalink]

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06 Dec 2017, 10:23
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Re: If the total income of a state increases by 50% and the population of   [#permalink] 06 Dec 2017, 10:23
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# If the total income of a state increases by 50% and the population of

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