by: Bunuel
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Difficulty:
75%
(hard)
Question Stats:
53% (02:14) correct
47%
(02:12)
wrong
based on 342
sessions
History
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Each student at a certain Mathematics exam either solved the hardest problem correctly or incorrectly. What percent of the examinees solved the hardest problem correctly?
(1) The average score of those students who solved the hardest problem correctly was 12 more than the average score of all students.
(2) The average score of those students who solved the hardest problem incorrectly was 3 less than the average score of all students.
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(1) The average score of those students who solved the hardest problem correctly was 12 more than the average score of all students.
(2) The average score of those students who solved the hardest problem incorrectly was 3 less than the average score of all students.
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Posts: 23
Total class score --> Mean Score*Total People --> M*P
Total score of the people who answered right --> (M+12)*N
Total score of the people who answered Wrong--> (M-3)*(P-N)
((M-3)*(P-N) + (M+12)*N) / P = M
MP-3P-MN+3N+MN+12N = PM
15N = 3P ( Rest of them cancel out)
N = 3/15 --> 20%
option -C
Total score of the people who answered right --> (M+12)*N
Total score of the people who answered Wrong--> (M-3)*(P-N)
((M-3)*(P-N) + (M+12)*N) / P = M
MP-3P-MN+3N+MN+12N = PM
15N = 3P ( Rest of them cancel out)
N = 3/15 --> 20%
option -C
Bunuel
Note :- I would take that the marks are 1 for correct and 0 for wrong and no negative marking..
Statements individually are not sufficient as they talk of a particular group to overall only..
So the combined will give us the answer..
C
To solve it, use weighted average method..
...Correct ....total......incorrect
..x+12.........x............x-3
Fraction of students answered correctly = \(\frac{x-(x-3)}{x+12-(x-3)}=\frac{3}{15}=\frac{1}{5}\)=20%
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General Discussion
chetan2u
Can you kindly help me with the weighted average calculation here?
How did you go from Correct Total Incorrect statement to the Fraction in the next sentence?
What I didnt understand is why correct and incorrect are at the extremes and why is X (the total) used in the middle to carry out the weighted average calculation.
Can you kindly help me with the weighted average calculation here?
How did you go from Correct Total Incorrect statement to the Fraction in the next sentence?
What I didnt understand is why correct and incorrect are at the extremes and why is X (the total) used in the middle to carry out the weighted average calculation.
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GMAT 1: 780 Q51 V45
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Expert reply
Bunuel
First, let's combine the information as the answer is obviously either C or E.
Let the percent of examinees who solved the hardest problem correctly be X. Then (1-X) percent did not solve it correctly.
Think of this as the scenario where we deduct the average score from every examinee. Then the students in statement 1 have an average score of 12, the students in statement 2 have an average score of -3. The total average would be 0. With this information we can come up with the equation: 12 * X - 3*(1 - X) = 0.
This equation uses the average score as a reference.
We may solve for X with the equation above so combined sufficient.
Ans: C
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Posts: 58
I haven't used the weighted average method but just created a equation for the average using information from both the options. I believe this is the quickest solution.
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