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Each student at a certain Mathematics exam either solved the hardest

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Bunuel
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Each student at a certain Mathematics exam either solved the hardest [#permalink] New post   07 Nov 2019, 02:53
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A
B
C
D
E

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85% (hard)

Question Stats:

51% (02:16) correct 49% (02:24) wrong based on 193 sessions
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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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C
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srikalivarapu
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Each student at a certain Mathematics exam either solved the hardest [#permalink] New post   25 Jun 2020, 12:39
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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
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chetan2u
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Re: Each student at a certain Mathematics exam either solved the hardest [#permalink] New post   07 Nov 2019, 21:20
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Bunuel wrote:
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.


Are You Up For the Challenge: 700 Level Questions


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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Each student at a certain Mathematics exam either solved the hardest [#permalink] New post   24 Jun 2020, 12:45
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.
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Each student at a certain Mathematics exam either solved the hardest [#permalink] New post   28 Jun 2020, 14:19
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Bunuel wrote:
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.


Are You Up For the Challenge: 700 Level Questions


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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Re: Each student at a certain Mathematics exam either solved the hardest [#permalink] New post   01 Sep 2022, 10:29
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Re: Each student at a certain Mathematics exam either solved the hardest [#permalink]
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