Brilliantia's Population

Algebra Level 3

On planet Brilliantia , exactly 35 35 % of the population lives in cities with more than 300000 300 000 inhabitants :

  • The largest city is Brilliantown with exactly 5045040 5045040 inhabitants.

  • The second largest city is Brilliantopolis wih half as many inhabitants as Brilliantown.

  • The population of the n n -th largest city follows exactly the rank-size rule i.e it has 1 n \frac{1}{n} -th as many inhabitants as the largest one (rounded to the nearest integer.)

How many people are there on Brilliantia ?

NB : If you feel there is not enough information to properly answer the question, you can submit 0 0 as your answer.


The answer is 48731180.

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1 solution

Romain Bouchard
Jan 24, 2018

We can notice that 5045040 17 < 300000 \frac{5045040}{17} < 300000 hence the population will be :

1 0.35 × 5045040 × k = 1 16 1 k = 48731180 \frac{1}{0.35} \times 5045040 \times \sum_{k=1}^{16} \frac{1}{k} = 48731180 .

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