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n: 64
S: 66
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
77% (02:38) correct
23%
(03:14)
wrong
based on 637
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A university professor teaches an introductory class with n students. On the first exam, the average (arithmetic mean) of the n scores of these students was exactly 72.5. After the exam, a new student transferred into the professor's class. The student had taken the same exam in another professor's class. The new average score on the exam, including the n scores of the original students, and the new student's score of S, was exactly 72.4.
Select for n and for S values that are jointly consistent. Make only 2 selections, one for each.
Select for n and for S values that are jointly consistent. Make only 2 selections, one for each.
| n | S | |
| 62 | ||
| 63 | ||
| 64 | ||
| 65 | ||
| 66 |
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Official Answer
n: 64
S: 66
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10 Dec 2024, 19:21
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Bismuth83
We know the average mean on the first exam = 72.5
No. of students = n
The sum of the scores on the first exam = 72.5n
As mentioned above after the exam a new student is transferred into the professor's class.
So. now the no.of the students would be n+1
The new student's score would be s The new average score on the exam including the n scores of the original students and the new student's score of s would be
72.5n + s/n+1 = 72.4
By solving the above equation we get 0.1n = 72.4 - s
Now, to equate the above equation we look at the values for n and s that best match up and we get the value for n as 64 and s as 66
Hence, n = 64 and s = 66
Updated on: 22 Feb 2025, 20:13
Originally posted by MartyMurray on 14 Feb 2025, 11:57.
Last edited by MartyMurray on 22 Feb 2025, 20:13, edited 2 times in total.
Last edited by MartyMurray on 22 Feb 2025, 20:13, edited 2 times in total.
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A university professor teaches an introductory class with n students. On the first exam, the average (arithmetic mean) of the n scores of these students was exactly 72.5. After the exam, a new student transferred into the professor's class. The student had taken the same exam in another professor's class. The new average score on the exam, including the n scores of the original students, and the new student's score of S, was exactly 72.4.
Select for n and for S values that are jointly consistent. Make only 2 selections, one for each.
Find the relationship between n and S
Average = Sum/Number
Average × Number = Sum
(Original Average × Original Number) + S = New Average × New Number
72.5n + S = 72.4(n + 1)
72.5n + S = 72.4n + 72.4
0.1n + S = 72.4
Find two values in the list that fit the relationship
62
63
64
65
66
Since all the values are integers, to get 4 in the tenths place in the sum of 0.1n + S, n must be 64 so that 0.1n has 4 in the tenths place.
Thus, n = 64, and S = 72.4 - 6.4 = 66.
Correct answer: 64, 66
Select for n and for S values that are jointly consistent. Make only 2 selections, one for each.
Find the relationship between n and S
Average = Sum/Number
Average × Number = Sum
(Original Average × Original Number) + S = New Average × New Number
72.5n + S = 72.4(n + 1)
72.5n + S = 72.4n + 72.4
0.1n + S = 72.4
Find two values in the list that fit the relationship
62
63
64
65
66
Since all the values are integers, to get 4 in the tenths place in the sum of 0.1n + S, n must be 64 so that 0.1n has 4 in the tenths place.
Thus, n = 64, and S = 72.4 - 6.4 = 66.
Correct answer: 64, 66
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