Difference between revisions of "1984 AIME Problems/Problem 10"

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== Problem ==
 
== Problem ==
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Mary told John her score on the American High School Mathematics Examination (AHSME), which was over <math>\displaystyle 80</math>. From this, John was able to determine the number of problems Mary solved correctly. If Mary's score had been any lower, but still over <math>\displaystyle 80</math>, John could not have determined this. What was Mary's score? (Recall that the AHSME consists of <math>\displaystyle 30</math> multiple choice problems and that one's score, <math>\displaystyle s</math>, is computed by the formula <math>\displaystyle s=30+4c-w</math>, where <math>\displaystyle c</math> is the number of correct answers and <math>\displaystyle w</math> is the number of wrong answers. Students are not penalized for problems left unanswered.)
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== Solution ==
 
== Solution ==
 
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Revision as of 00:18, 21 January 2007

Problem

Mary told John her score on the American High School Mathematics Examination (AHSME), which was over $\displaystyle 80$. From this, John was able to determine the number of problems Mary solved correctly. If Mary's score had been any lower, but still over $\displaystyle 80$, John could not have determined this. What was Mary's score? (Recall that the AHSME consists of $\displaystyle 30$ multiple choice problems and that one's score, $\displaystyle s$, is computed by the formula $\displaystyle s=30+4c-w$, where $\displaystyle c$ is the number of correct answers and $\displaystyle w$ is the number of wrong answers. Students are not penalized for problems left unanswered.)

Solution

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See also

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