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

Question

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%

gmate2010 · Answer

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

Economist · Answer

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

TheRob · Answer

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?

EMPOWERgmatRichC · Answer

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:  C

GMAT assassins aren't born, they're made,
Rich

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