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In a contest, two people will have to answer 100 questions each. They score 1 point for each correct answer. The contest has not ended yet. Each person has already answered 90 questions. Person A has answered 60% of the first 90 questions correctly. Person B has answered 50% of the first 90 questions correctly. What is the minimum number of points that Person A must get from the last 10 questions to win the contest?

May 26, 2022

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In a contest, two people will have to answer 100 questions each. They score 1 point for each correct answer. The contest has not ended yet. Each person has already answered 90 questions. Person A has answered 60% of the first 90 questions correctly. Person B has answered 50% of the first 90 questions correctly. What is the minimum number of points that Person A must get from the last 10 questions to win the contest?

Person B has answered 45 questions correctly.  (90 x .50)

If B gets all ten of the remaining correct, B will then have 55.

Person A has answered 54 questions correctly.  (90 x .60)

The best B can do is 55, so A needs 56 to guarantee a defeat of B.

So A needs a minimum of 2 more correct answers to nail down the win.

Of course, B might not get all ten remaining questions correct,

in which case A could prevail with fewer than 2 more correct answers.

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May 26, 2022