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The population of City $\mathrm{X}$ increased from 2 million in the year 2000 to $2.5$ million in 2015 and the gross domestic product of the city in 2000 was $\frac{3}{8}$ less than that in 2015 . What was the approximate percent change, rounded to the nearest integer if required, in the per capita gross domestic product of the city from 2000 to $2015 ?$
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We know that 'the gross domestic product of the city in 2000 was $\frac{3}{8}$ less than that in 2015 ,'so let's assume that the GDP in 2015 was 800 ; thus, the GDP in the year $2000=800-\frac{3}{8} \times 800=500$.

We assumed a seemingly puzzling number '800' for the GDP in 2015 since we find that in the denominator of the fraction $\frac{3}{8}$, we have to deal with ' 8, ' and ' 800 ' is a multiple of ' 8 ' - easy to deal with.
We know that the population year $2000=2 \mathrm{M}$ and that in $2015=2.5 \mathrm{M}$
Thus,
Per capita GDP in $2000=\frac{\text { GDP }}{\text { population }}=\frac{500}{2 \mathrm{M}}=\frac{250}{\mathrm{M}}$ and
Per capita GDP in $2005=\frac{\text { GDP }}{\text { population }}=\frac{800}{2.5 \mathrm{M}}=\frac{8000}{25 \mathrm{M}}=\frac{320}{\mathrm{M}}$
Thus,
\begin{aligned} & \text { Change in Per Capita GDP over 2000-2015 }=\frac{\text { (Per Capita GDP in 2015)-(Per Capita GDP in 2000) }}{\text { (Per Capita GDP in 2000) }} \times 100 \% \\ & =\frac{\frac{320}{\mathrm{M}}-\frac{250}{\mathrm{M}}}{\frac{250}{\mathrm{M}}} \times 100 \% \\ & =\frac{70}{250} \times 100 \% \text { (M gets cancelled) } \\ & =28 \% \end{aligned}
by Diamond (50,291 points)

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