HMMT 十一月 2015 · 冲刺赛 · 第 4 题

HMMT November 2015 — Guts Round — Problem 4

[ 6 ] Eric is taking a biology class. His problem sets are worth 100 points in total, his three midterms are worth 100 points each, and his final is worth 300 points. If he gets a perfect score on his problem sets and scores 60% , 70% , and 80% on his midterms respectively, what is the minimum possible percentage he can get on his final to ensure a passing grade? (Eric passes if and only if his overall percentage is at least 70%).

解析

[ 6 ] Eric is taking a biology class. His problem sets are worth 100 points in total, his three midterms are worth 100 points each, and his final is worth 300 points. If he gets a perfect score on his problem sets and scores 60% , 70% , and 80% on his midterms respectively, what is the minimum possible percentage he can get on his final to ensure a passing grade? (Eric passes if and only if his overall percentage is at least 70%). Proposed by: Alexander Katz Answer: 60% We see there are a total of 100 + 3 × 100 + 300 = 700 points, and he needs 70% × 700 = 490 of them. He has 100 + 60 + 70 + 80 = 310 points before the final, so he needs 180 points out of 300 on the final, which is 60%.