1986 AHSME Problems/Problem 12
Problem
John scores on this year's AHSME. Had the old scoring system still been in effect, he would score only for the same answers. How many questions does he leave unanswered? (In the new scoring system that year, one receives points for each correct answer, points for each wrong answer, and points for each problem left unanswered. In the previous scoring system, one started with points, received more for each correct answer, lost point for each wrong answer, and neither gained nor lost points for unanswered questions.)
Solution
Let , , and be the number of correct, wrong, and unanswered questions respectively. From the old scoring system, we have , from the new scoring system we have , and since there are problems in the AHSME, . Solving the simultaneous equations yields , which is .
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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