Question 1195348: A certain university classified students as freshmen, sophomores, juniors, seniors, or graduate level. The mean number of students per classification is 6,000. If students classified as graduate level are excluded from the calculation, the mean number of students per classification is 7,000. Which of the following could be the number of students classified as graduate level?
A) 1,000
B) 2,000
C) 4,000
D) 5,000
Answer by math_tutor2020(3817)   (Show Source):
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A = number of freshmen
B = number of sophomores
C = number of juniors
D = number of seniors
E = number of graduate level students
Add up all those population counts and divide by 5 to determine the average. We're told the average is 6000 which means:
(A+B+C+D+E)/5 = average
(A+B+C+D+E)/5 = 6000
A+B+C+D+E = 5*6000
A+B+C+D+E = 30,000
We're also told that if we exclude the graduate level, then the average becomes 7000 per class level
So,
(A+B+C+D)/4 = 7000
A+B+C+D = 4*7000
A+B+C+D = 28,000
Let's use that in the previous equation found earlier
A+B+C+D+E = 30,000
(A+B+C+D)+E = 30,000
(28,000)+E = 30,000
E = 30,000 - 28,000
E = 2,000
The wording of "Which of the following could be the number of students classified as graduate level?" should instead be "Which of the following is the number of students classified as graduate level?" because there's only one possible value for E. The "could" makes it seem like other answers are possible, which isn't the case.
Answer: B) 2,000
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