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, 2009

Combinatorics Difficulty 2.0 Junior Find the answer Canada

At Matilda's birthday party, the ratio of people who ate ice cream to people who ate cake was $3:2$ . People who ate both ice cream and cake were included in both categories. If 120 people were at the party, what is the maximum number of people who could have eaten both ice cream and cake?

(A) $24$ (B) $30$ (C) $48$ (D) $80$ (E) $72$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.