2011 AMC 12A Problem 5

Below is the professionally curated solution for Problem 5 of the 2011 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 12A solutions, or check the answer key.

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Concepts:percentage conditional probability

Difficulty rating: 990

Last summer $30\%$ of the birds living on Town Lake were geese, $25\%$ were swans, $10\%$ were herons, and $35\%$ were ducks. What percent of the birds that were not swans were geese?

$20$

$30$

$40$

$50$

$60$

Solution:

The birds that are not swans make up $100\% - 25\% = 75\%$ of the total, and geese are $30\%$ of the total. The requested fraction is $\dfrac{30}{75} = \dfrac{2}{5} = 40\%.$

Thus, the correct answer is C.

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