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2007 AMC 12B Problem 5

Problem 5 of 25EasierAlgebra

The 20072007 AMC 1212 contests will be scored by awarding 66 points for each correct response, 00 points for each incorrect response, and 1.51.5 points for each problem left unanswered. After looking over the 2525 problems, Sarah has decided to attempt the first 2222 and leave the last 33 unanswered. How many of the first 2222 problems must she solve correctly in order to score at least 100100 points?

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Solution

The three unanswered problems give 3⋅1.5=4.53\cdot1.5=4.5 points. So Sarah needs at least 100−4.5=95.5100-4.5=95.5 points from correct answers. Since 15<95.56<16, 15\lt\dfrac{95.5}{6}\lt16, she must solve at least 1616 problems correctly, which would give her 16⋅6+4.5=100.516\cdot6+4.5=100.5 points. Thus, the correct answer is D.
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