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

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Intern
Joined: 14 Oct 2018
Posts: 18

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01 Jun 2019, 06:37
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Difficulty:

55% (hard)

Question Stats:

50% (02:48) correct 50% (01:15) wrong based on 16 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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NUS School Moderator
Joined: 18 Jul 2018
Posts: 1026
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)

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01 Jun 2019, 07:23
1
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.

VP
Joined: 19 Oct 2018
Posts: 1174
Location: India

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01 Jun 2019, 12:44
1
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
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