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A group of students took an exam that was scored from 0 to 1
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21 May 2020, 10:37
21 May 2020, 10:37
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A group of students took an exam that was scored from 0 to 100 points. 70 percent of the students in the group passed the exam, and these students received an average score of 86. The average score on the exam for the entire group was 74.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The median score on the exam for the entire group of students |
Two times the average score of all the students who did not pass the exam |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Re: A group of students took an exam that was scored from 0 to 1
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05 Jan 2021, 10:08
05 Jan 2021, 10:08
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Carcass wrote:
A group of students took an exam that was scored from 0 to 100 points. 70 percent of the students in the group passed the exam, and these students received an average score of 86. The average score on the exam for the entire group was 74.
Quantity A |
Quantity B |
The median score on the exam for the entire group of students |
Two times the average score of all the students who did not pass the exam |
We can apply the weighted averages formula here...
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
Let x = the average score of the students who FAILED the exam.
We can write: 74 = (0.7)(86) + (0.3)(x)
Expend: 74 = 60.2 + 0.3x
Subtract 60.2 from both sides of the equation to get: 13.8 = 0.3x
Solve: x = 13.8/0.3 = 46
So, 46 is the average score of the students who failed the exam
Consider these two conflicting cases:
case i: There are 100 students in total, 30 students all scored exactly 46, and the remaining 70 students all scored exactly 86
In this case, the median score for the entire group = 86
And the average score of all the students who failed the exam = 46
We get:
QUANTITY A: 86
QUANTITY B: 2(46) = 92
In this case, Quantity B is greater
case ii: There are 100 students in total, and 30 students all scored exactly 46. 18 of the remaining students all scored exactly 60, and the remaining 52 students scored 95 (these values meet the condition that the students who passed the exam have an average score of 86)
In this case, the median score for the entire group = 95
And the average score of all the students who failed the exam = 46
We get:
QUANTITY A: 95
QUANTITY B: 2(46) = 92
In this case, Quantity A is greater
Answer: D
General Discussion
Re: A group of students took an exam that was scored from 0 to 1
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27 May 2020, 21:19
27 May 2020, 21:19
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We can find the average score of the students who did not pass:
For the 70% that did pass : 0.7x (x is the total number of students)
86 = sum(passing scores)/0.7x
sum(passing scores) = 60.2x
Then we can find the sum(all scores), using x as 100% of the students
74 = sum(all scores)/x
sum(all scores) = 74x
If we remove the passing scores from all scores we get the sum(failing scores)
sum(all scores) - sum(passing scores) = sum(failing scores)
74x - 60.2x = 13.8x
And the average score
avg = 13.8x/(0.3x) = 46
But since 46 * 2 = 92 , this is in the range of "passing scores", so we don't know whether the median score of all students is greater or less than this. (if it were below the range of passing scores, we could say option A is correct, since we know that 70% will include the median)
Then, the answer is D
For the 70% that did pass : 0.7x (x is the total number of students)
86 = sum(passing scores)/0.7x
sum(passing scores) = 60.2x
Then we can find the sum(all scores), using x as 100% of the students
74 = sum(all scores)/x
sum(all scores) = 74x
If we remove the passing scores from all scores we get the sum(failing scores)
sum(all scores) - sum(passing scores) = sum(failing scores)
74x - 60.2x = 13.8x
And the average score
avg = 13.8x/(0.3x) = 46
But since 46 * 2 = 92 , this is in the range of "passing scores", so we don't know whether the median score of all students is greater or less than this. (if it were below the range of passing scores, we could say option A is correct, since we know that 70% will include the median)
Then, the answer is D
