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Question 14

A competition has $$25$$ questions and is marked as follows. 

Solution

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The maximum score is $$15\cdot5+10\cdot6=135$$. A score of $$129$$ is obtained by leaving one six-mark question unanswered, $$128$$ by making one incorrect answer in the first negative-mark group, and $$127$$ by making one incorrect answer in the second negative-mark group. Thus $$126$$ is the only listed score that cannot be achieved.

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