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27 Jun 2022, 01:30
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Difficulty:
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57% (02:45) correct
43%
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based on 86
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On Monday, 9 students each took a test with 100 questions. The average (arithmetic mean) number of correct answers was 50, and the median number of correct answers was 40. With of the following statements must be true?
I. At least one student had more than 60 correct answers.
II. At least one student had more than 40 and less than 50 correct answers.
III. At least one student had less than 40 correct answers.
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III
Are You Up For the Challenge: 700 Level Questions
I. At least one student had more than 60 correct answers.
II. At least one student had more than 40 and less than 50 correct answers.
III. At least one student had less than 40 correct answers.
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III
Are You Up For the Challenge: 700 Level Questions
27 Jun 2022, 03:18
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No. of students = 9
Mean = 50
Sum = 450
Median (5th term in ascending order) = 40
I. At least one student had more than 60 correct answers.
To check if there is a figure of greater than 60 (which is greater than the mean), we should maximize the terms leading up to the median
Now, since the 5th term (median) is 40, our first 4 terms can not be greater than that so maximum we can have is 40 as the first 5 terms so a sum of 200
Sum of remaining 4 terms = 450-200 = 250, so average of remaining 4 terms is 62.5 so atleast one student will have greater than 60 correct answers
II. At least one student had more than 40 and less than 50 correct answers.
Same case as in the previous statement
40 40 40 40 40 and if we have 62 63 62 63 that satisfies both mean and median and not true to have between 40 and 50 correct answers
III. At least one student had less than 40 correct answers.
Same case as in the previous statement
40 40 40 40 40 and if we have 62 63 62 63 that satisfies both mean and median and not true to have one student with less than 40 correct answers
Answer - A
Mean = 50
Sum = 450
Median (5th term in ascending order) = 40
I. At least one student had more than 60 correct answers.
To check if there is a figure of greater than 60 (which is greater than the mean), we should maximize the terms leading up to the median
Now, since the 5th term (median) is 40, our first 4 terms can not be greater than that so maximum we can have is 40 as the first 5 terms so a sum of 200
Sum of remaining 4 terms = 450-200 = 250, so average of remaining 4 terms is 62.5 so atleast one student will have greater than 60 correct answers
II. At least one student had more than 40 and less than 50 correct answers.
Same case as in the previous statement
40 40 40 40 40 and if we have 62 63 62 63 that satisfies both mean and median and not true to have between 40 and 50 correct answers
III. At least one student had less than 40 correct answers.
Same case as in the previous statement
40 40 40 40 40 and if we have 62 63 62 63 that satisfies both mean and median and not true to have one student with less than 40 correct answers
Answer - A
27 Jun 2022, 03:56
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If we order the 9 students' scores from the lowest to the highest, we know that their average is 50, so total is 450.
The fifth student has a score of 40.
I. At least one student had more than 60 correct answers.
Let's see the highest possible sum of the 9 students if no student has more than 60 correct answers. The highest possible sum of
40 40 40 40 40 59 59 59 59
= 436 < total of 450
So, At least one student had more than 60 correct answers.
II. At least one student had more than 40 and less than 50 correct answers.
Not necessarily. For example:
38 40 40 40 40 63 63 63 63
III. At least one student had less than 40 correct answers.
Not necessarily. For example:
40 40 40 40 40 62 62 62 64
The answer is thus (A).
The fifth student has a score of 40.
I. At least one student had more than 60 correct answers.
Let's see the highest possible sum of the 9 students if no student has more than 60 correct answers. The highest possible sum of
40 40 40 40 40 59 59 59 59
= 436 < total of 450
So, At least one student had more than 60 correct answers.
II. At least one student had more than 40 and less than 50 correct answers.
Not necessarily. For example:
38 40 40 40 40 63 63 63 63
III. At least one student had less than 40 correct answers.
Not necessarily. For example:
40 40 40 40 40 62 62 62 64
The answer is thus (A).
