The course grade for a mathematics course consists of 60 percent of the final-exam grade plus 20 percent of each of two preliminary exam grades, where each exam grade is a number from 0 through 100. If a student's course grade must be at least 60 in order for the student to pass the course, did Greg pass the course?(1) Greg's final-exam grade was greater than 50.
This means the final-exam contributed more than 0.6 * 50 = 30 points out of the required 60. Not sufficient.
(2) The average (arithmetic mean) of Greg's two preliminary exam grades was greater than 68.
This implies the sum of the two grades was greater than 2 * 68 = 136, contributing more than 0.2 * 136 = 27.2 points out of the required 60. Not sufficient.
(1) + (2) Together, Greg's course grade would be more than 30 + 27.2 = 57.2. Therefore, the grade could have been less than or greater than 60. Not sufficient.
Answer: E.