In a competitive examination, the Data Insight section consists of 20

Question

In an examination, the Data Insights section has 20 questions. Each correct answer awards 3 points, while each incorrect answer results in a 1-point deduction, and there is no penalty for unanswered questions. During his only attempt, Paul scored 35 points on this section.

Based on the above information, select for  Unattempted  the maximum number of questions that Paul could have left unanswered and for  Incorrect  the maximum number of questions that Paul could have answered incorrectly and still scored 35 points.

Bunuel · Accepted Answer

Official Solution: To maximize the number of questions that Paul could have left unanswered, we should minimize the number of correct and incorrect answers. The minimum number of questions Paul could have answered correctly to score 35 is 12. In this case, he would have earned 3 * 12 = 36 points, so he must have answered one question incorrectly to reduce the score to 35. This results in a total of 12 + 1 = 13 correct and incorrect answers, making the maximum number of unanswered questions equal to 7. To get the maximum number of questions Paul could have answered incorrectly, let's check the options: 8 incorrect would result in -8 points, meaning 43 points would need to be gained with correct answers, which is not possible (43 is not a multiple of 3). 7 incorrect would result in -7 points, meaning 42 points would need to be gained with correct answers, requiring 14 correct answers. This is not possible because 7 + 14 > 20. 6 incorrect would result in -6 points, meaning 41 points would need to be gained with correct answers, which is not possible (41 is not a multiple of 3). 5 incorrect would result in -5 points, meaning 40 points would need to be gained with correct answers, which is not possible (40 is not a multiple of 3). 4 incorrect would result in -4 points, meaning 39 points would need to be gained with correct answers, requiring 13 correct answers. This is possible with the addition of 3 unanswered questions: 4 + 13 + 3 = 20. Therefore, the maximum number of questions Paul could have answered incorrectly is 4. Correct answer: Unattempted "7" Incorrect "4" GMAT-Club-Forum-dx18l9i3.png

Kinshook · Answer

In a competitive examination, the Data Insight section consists of 20 questions. Every correct answer gets the student three marks while there is a negative marking of one mark for each wrong answer. There is no penalty for an unanswered question.

Paul gets a net score of 35 marks in the DI section.

Based on the above information, select for  Unattempted  the maximum number of questions that Paul could have left unanswered and for  Incorrect  the maximum number of questions that Paul could have answered incorrectly and still got 35 marks.

Solutions: -

Status  Number of questions  Marks/question  Marks  
  Incorrect  x  -1  -x  
  Unanswered  u  0  0  
  Correct  20-x-u  3  3(20-x-u) = 60-3x-3u

Net score = -x + (60-3x-3u) = 60 - 4x -3u = 35
4x + 3u = 25

For maximum number of questions that Paul could have left unanswered (u)
u = 7; x = 1
The maximum number of questions that Paul could have left unanswered and still got 35 marks = 7

For maximum number of questions that Paul could have answered incorrectly (x)
x = 4; u = 3
The maximum number of questions that Paul could have answered incorrectly and still got 35 marks = 4

brp616 · Answer

Again, I love DI but maybe its just because of my work/former LSAT self.

So, we know
C/correct = 3
I/incorrect = -1
N/not answered = 0

We need to maximize the number of I and Ns to get a net score of 35

Let's start with not answered, that seemed simple enough. Basically, we need to reach 35 in the least number of C/I then give the rest of the remaining questions of 20 to not answered.

To reach 35 points we need at least 12 correct questions, as 12 * 3 = 36, which is the lowest positive point value we can get above 35.
If we have 12 correct we need 1 incorrect to get 36 - 1 = 35, which leaves us with 7 remaining questions to leave unanswered and there's our answer for that!

Max incorrect is a little more complex, but basically trying to use the most Cs/Is possible within 20 questions. So let's build on our work from the last problem

12 correct: 1 incorrect, 7 unanswered
13 correct (39 points), 4 incorrect (-4), 3 left unanswered - 35 net points
14 correct (42 points)... this leaves us with 6 questions, but we need -7 to reach 35 so this is impossible, so we have to go with the above solution
13 correct, 4 incorrect, 3 unanswered so our max incorrect is 4!

vishal_gupta · Answer

To get max unattempted questions we have to minimize correct and incorrect number of questions. 
So, correct no. of questions=12 and incorrect=1.
 Unattempted max= 7

To get max incorrect we have to get min no of unattempted questions.
If correct=14, then we have to get 7 incorrect for 35 marks. Not possible as total questions=20
If correct=13 then we have to get 4 incorrect.

Hence max incorrect questions= 4

Catman · Answer

In a competitive examination, the Data Insight section consists of 20 questions. Every correct answer gets the student three marks while there is a negative marking of one mark for each wrong answer. There is no penalty for an unanswered question.

Paul gets a net score of 35 marks in the DI section.

Based on the above information, select for Unattempted the maximum number of questions that Paul could have left unanswered and for Incorrect the maximum number of questions that Paul could have answered incorrectly and still got 35 marks.

Let c - correct, i-incorrect and u-unattempted question.

c+i+u=20
3c-i = 35

To achieve 35 score, minimum 12 questions to be answered. c>=12
Maximum unattempted will be when minimum incorrect and minimum correct , incorrect can not be 0 as score is odd, so minimum incorrect =1 and Correct = 12
 Maximum unattempted  =  7  .

Maximum incorrect will be when minimum unattempted and minimum correct , unattempted can not be 0 as For c=14, i= 7, and u=0 (This case not possible as total question =20)
This implies c should be less than 14, for c=13, i=4 and u=3

Maximum incorrect  =  4

KarishmaB · Answer

To maximize unattempted, we need to minimise correct and incorrect questions. 
To score 35, one must get at least 12 questions correct (which give a score of 36) and then 1 question incorrect for 1 negative marking to get a final score of 35.
Hence 13 questions must be attempted.

Max 7 questions can be unattempted.

To maximize incorrect questions maximum questions should be attempted. 
Say 15 are correct and 5 incorrect. But then the score is 45 - 5 = 40 (too high)
Say 14 are correct and 6 incorrect. But then the score is 42 - 6 = 36 (too high)
Say 13 are correct and 7 incorrect. But then the score is 39 - 7 = 32 (too low)
So we can't get 35 without leaving some questions unattempted. Then 13 could be correct, 4 incorrect and 3 unattempted.

Max 4 questions incorrect.

unraveled · Answer

The nearest number to 35 which is multiple of 3 is 36. This means that the minimum number of questions that needs to be attempted is 12.
Further, this means one questions needs to be incorrect. But if that happens 33 is score (11*3). 
If 13 are correct attempted then  4 questions are to be incorrect  so that score is 35 - 3 remains unattempted.
For unattempted too Paul needs to attempt 13 questions where 12 are correct and 1 incorrect. The  rest 7 remain unattempted.

Unattempted = 7
Incorrect = 4

Atharv2608 · Answer

in these kind of questions, how do we decide that the maximums have to be the maximum in their own respective cases and not mutually, ie how do we decide wether we have to maximise both unattempted and incorrect together in the same scenario, or do them independantly for 2 deparate situations? I remember doing a question where the language did not imply to do them together, but the correct answer ended up being to minimise both of them in the same context?? I would normally do them independently, but this format of questioning has me confused? As a general rule , can i go ahead with just always doing them independantly?

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In a competitive examination, the Data Insight section consists of 20

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Status	Number of questions	Marks/question	Marks
Incorrect	x	-1	-x
Unanswered	u	0	0
Correct	20-x-u	3	3(20-x-u) = 60-3x-3u

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