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01 Apr 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (01:50) correct
31%
(01:58)
wrong
based on 331
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The students in a certain college class took a midterm exam and a final exam, both of which were scored out of a total of 100 points. What percent of the students earned a higher score on the final than on the midterm?
(1) Of the students in the class, 28% scored at least 6 points higher on the final than on the midterm.
(2) Of the students who scored higher on the final than on the midterm, 40% scored at least 6 points higher on the final.
(1) Of the students in the class, 28% scored at least 6 points higher on the final than on the midterm.
(2) Of the students who scored higher on the final than on the midterm, 40% scored at least 6 points higher on the final.
01 Apr 2024, 06:17
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Answer C
1: 28% score at least 6points higher on the final exam
We don’t know how many percent score between 1point and 5 points higher on the final exam
Insufficient
2- of the students who scored higher on the final exam than the midterm exam, 40% score at least 6 points higher on the final.
%student score at least 6points higher +% students who score higher than 0 and lesser than 6 + %student who score the same on both tests + % who scored less on the final =100%
Less have X% student score more on the final exam
40%(X%) = 28% total students (more than 6 points)
60% (X%) should be equal to 42%
Hence total students who scored more on the final is 42% + 28%= 70%
Posted from my mobile device
1: 28% score at least 6points higher on the final exam
We don’t know how many percent score between 1point and 5 points higher on the final exam
Insufficient
2- of the students who scored higher on the final exam than the midterm exam, 40% score at least 6 points higher on the final.
%student score at least 6points higher +% students who score higher than 0 and lesser than 6 + %student who score the same on both tests + % who scored less on the final =100%
Less have X% student score more on the final exam
40%(X%) = 28% total students (more than 6 points)
60% (X%) should be equal to 42%
Hence total students who scored more on the final is 42% + 28%= 70%
Posted from my mobile device
24 Sep 2024, 08:01
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We need to find the percent of students who earned a higher score on the final than on the midterm.
Statement (1): Of the students in the class, 28% scored at least 6 points higher on the final than on the midterm.
This tells us that 28% of students improved by 6 or more points.
However, it doesn't tell us about students who improved by less than 6 points.
Therefore, this statement alone is not sufficient.
Statement (2): Of the students who scored higher on the final than on the midterm, 40% scored at least 6 points higher on the final.
This tells us about the proportion of students who improved significantly (by 6 or more points) among those who improved at all.
However, it doesn't tell us what percentage of the total class improved their scores.
Therefore, this statement alone is not sufficient.
3) Now, let's consider both statements together:
From (1), we know that 28% of all students improved by 6 or more points.
From (2), we know that these students who improved by 6 or more points represent 40% of all students who improved.
We can set up an equation: 28% = 40% * x, where x is the percentage of all students who improved.
Solving this: x = 28% / 40% = 0.7 = 70%
Therefore, combining both statements, we can determine that 70% of students earned a higher score on the final than on the midterm.
The correct answer is (C) - Both statements together are sufficient to answer the question.
Statement (1): Of the students in the class, 28% scored at least 6 points higher on the final than on the midterm.
This tells us that 28% of students improved by 6 or more points.
However, it doesn't tell us about students who improved by less than 6 points.
Therefore, this statement alone is not sufficient.
Statement (2): Of the students who scored higher on the final than on the midterm, 40% scored at least 6 points higher on the final.
This tells us about the proportion of students who improved significantly (by 6 or more points) among those who improved at all.
However, it doesn't tell us what percentage of the total class improved their scores.
Therefore, this statement alone is not sufficient.
3) Now, let's consider both statements together:
From (1), we know that 28% of all students improved by 6 or more points.
From (2), we know that these students who improved by 6 or more points represent 40% of all students who improved.
We can set up an equation: 28% = 40% * x, where x is the percentage of all students who improved.
Solving this: x = 28% / 40% = 0.7 = 70%
Therefore, combining both statements, we can determine that 70% of students earned a higher score on the final than on the midterm.
The correct answer is (C) - Both statements together are sufficient to answer the question.
