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Each student at a certain Mathematics exam either solved the hardest

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Each student at a certain Mathematics exam either solved the hardest  [#permalink]

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New post 07 Nov 2019, 02:53
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

47% (02:56) correct 53% (01:51) wrong based on 14 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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Re: Each student at a certain Mathematics exam either solved the hardest  [#permalink]

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New post 07 Nov 2019, 21:20
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.


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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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Re: Each student at a certain Mathematics exam either solved the hardest   [#permalink] 07 Nov 2019, 21:20
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Each student at a certain Mathematics exam either solved the hardest

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