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Math Expert V
Joined: 02 Sep 2009
Posts: 60630
Each student at a certain Mathematics exam either solved the hardest  [#permalink]

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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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Math Expert V
Joined: 02 Aug 2009
Posts: 8336
Re: Each student at a certain Mathematics exam either solved the hardest  [#permalink]

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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%
_________________ 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  