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BMAT 2009 · Question 18 · Logic

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In the Beijing Olympics, in 2008, China claimed to have come out top of the medal rankings on the basis that it won the most gold medals. The USA contested this on the grounds that it won the most medals, gold, silver and bronze counting one each. But arguably neither of the above methods of counting gives an accurate picture of relative achievement. The fairest system would be weighting the medals, as follows, and/or comparing the medals won against population or national wealth.

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Great Britain came 4th in the ranking on all three methods of counting (figs 1 - 3). If the ranking had been based on the proportion of gold medals to all medals, among China, the USA, the Russian Federation and Great Britain, where would Great Britain have ranked?