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CAT 2017 paper had 100 questions. Each correct answer was aw

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Intern
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Joined: 14 Oct 2018
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CAT 2017 paper had 100 questions. Each correct answer was aw  [#permalink]

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New post 01 Jun 2019, 06:37
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Question Stats:

38% (02:39) correct 62% (01:15) wrong based on 13 sessions

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CAT 2017 paper had 100 questions. Each correct answer was awarded 3
marks and each wrong answer was penalized 1 negative mark. If certain number of aspirants attempted different number of questions but each one of them obtained the same overall score of 56, what is the largest possible size of this group of people?

(A) 21
(B) 16
(C) 19
(D) 14
(E) 25

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CAT 2017 paper had 100 questions. Each correct answer was aw  [#permalink]

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New post 01 Jun 2019, 07:23
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1
Each correct ans - 3 marks
Each Incorrect ans - -1 marks
Final marks of 56 is not divisible by 3, hence minimum of 1 incorrect ans occurs.
Number of correct ans - 19*3 = 57 and 1 Incorrect. = 57-1 = 56 marks.
Next possible value is 20 correct and 4 Incorrect. = 20*3 = 60-4 = 56.
Next value is (21-Correct, 7-Incorrect), (22-Correct, 10-Incorrect)........(39-Correct, 61-Incorrect) Untill the total number of question attended is 100.

Total number of students possible is 21.

A is the answer
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CAT 2017 paper had 100 questions. Each correct answer was aw  [#permalink]

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New post 01 Jun 2019, 12:44
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Let number of correct questions=a, and number of wrong question=b
3a-b=56
and a+b≤100

3a=b+56
minimum value a can take, when b is minimum
3a=1+56
minimum value of a=19

maximum value a can take, when b=100-a
3a-100+a=56
4a=156
a=39

largest possible size of this group of people= (39-19)+1=21


Rajat1998 wrote:
CAT 2017 paper had 100 questions. Each correct answer was awarded 3
marks and each wrong answer was penalized 1 negative mark. If certain number of aspirants attempted different number of questions but each one of them obtained the same overall score of 56, what is the largest possible size of this group of people?

(A) 21
(B) 16
(C) 19
(D) 14
(E) 25

Posted from my mobile device
GMAT Club Bot
CAT 2017 paper had 100 questions. Each correct answer was aw   [#permalink] 01 Jun 2019, 12:44
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CAT 2017 paper had 100 questions. Each correct answer was aw

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