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UKMT Junior Kangaroo, 2018

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A box contains seven cards, each with a different integer from $1$ to $7$ written on it. Avani takes three cards from the box and then Niamh takes two cards, leaving two cards in the box. Avani looks at her cards and then tells Niamh "I know the sum of the numbers on your cards is even." What is the sum of the numbers on Avani's cards?

(A) $6$ (B) $9$ (C) $10$ (D) $11$ (E) $12$

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