2011 AMC 10A Problem 8

Below is the professionally curated solution for Problem 8 of the 2011 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 10A solutions, or check the answer key.

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Concepts:percentage ratio and proportion

Difficulty rating: 870

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:

WLOG, let there be a $100$ birds. Then $75$ birds are not swans. The desired percentage is then $\dfrac{30}{75} \cdot 100 = 40 \%.$

Thus, C is the correct answer.

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