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QUESTION:
In a class of 80 students, Jim’s score on Exam 1 is higher than 65% of the students of the class. On Exam 2, his score is higher than 75% of the students. On both exams, Jim’s scores are unique. If the scores from the two tests are added, what is the minimum number of students whose total scores are below Jim’s?
EXPLANATION:
On Exam 1, the number of students that scored below Jim is 80 × (65/100) = 52 and the number of students that scored more than him,since his score is unique, is 79 – 52 = 27. There are 79 students excluding him. These numbers are 80 × (75/100) = 60 and 79- 60 = 19, respectively, for Exam 2. Since the exact scores are unknown, any student who has scored more than Jim in one exam and less than Jim in the other, may or may not have a total score less than his. Only students who scored less than him in both exams will certainly have a total score less than his. We need to find the minimum number of such students. If all 27 students that scored above him on Exam 1 are assumed to have scored less than him on Exam 2, there will still be 60 – 27 = 33 students that scored below him on both exams, and these students will certainly have a lower total score.
My problem:
WHY can we assume that the 27 that scored higher than him on the first exam did not on the second exam? The first exam had 27, the second 19, how can you safely assume that none of the 27 were apart of the second 19??
BTW this is exactly why I HATE QR.
In a class of 80 students, Jim’s score on Exam 1 is higher than 65% of the students of the class. On Exam 2, his score is higher than 75% of the students. On both exams, Jim’s scores are unique. If the scores from the two tests are added, what is the minimum number of students whose total scores are below Jim’s?
EXPLANATION:
On Exam 1, the number of students that scored below Jim is 80 × (65/100) = 52 and the number of students that scored more than him,since his score is unique, is 79 – 52 = 27. There are 79 students excluding him. These numbers are 80 × (75/100) = 60 and 79- 60 = 19, respectively, for Exam 2. Since the exact scores are unknown, any student who has scored more than Jim in one exam and less than Jim in the other, may or may not have a total score less than his. Only students who scored less than him in both exams will certainly have a total score less than his. We need to find the minimum number of such students. If all 27 students that scored above him on Exam 1 are assumed to have scored less than him on Exam 2, there will still be 60 – 27 = 33 students that scored below him on both exams, and these students will certainly have a lower total score.
My problem:
WHY can we assume that the 27 that scored higher than him on the first exam did not on the second exam? The first exam had 27, the second 19, how can you safely assume that none of the 27 were apart of the second 19??
BTW this is exactly why I HATE QR.
