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The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. One of the students found that his score

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by M7MBA » Wed Jun 24, 2020 6:47 am

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The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. One of the students found that his score was less by \(‘x’\) points due to a calculation error. If the average of three score increases by 3 points after correcting this error and the median score remains the same before and after correction, which of the following could be the range of list of corrected scores?

A 2
B 5
C 7
D 11
E 20

[spoiler]OA=E[/spoiler]

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Re: The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. One of the students found that his sc

by Scott@TargetTestPrep » Mon Jun 29, 2020 9:06 am
M7MBA wrote: ↑
Wed Jun 24, 2020 6:47 am
 The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. One of the students found that his score was less by \(‘x’\) points due to a calculation error. If the average of three score increases by 3 points after correcting this error and the median score remains the same before and after correction, which of the following could be the range of list of corrected scores?

A 2
B 5
C 7
D 11
E 20

[spoiler]OA=E[/spoiler]

Solution:


Before the error is corrected, the average is (21 + 25 + 32)/3 = 78/3 = 26. Therefore, after the error is corrected, the average is 29. Since the new total is 29 x 3 - 26 x 3 = 87 - 78 = 9 points higher than the old total, the 9 points must be added to one and only one student’s score. However, since the median does not change, the 9 points must be added to 32 so that it becomes 41. Therefore, the range of the corrected scores 41 - 21 = 20.

Answer: E

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