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 June 3rd, 2019, 04:19 PM #1 Senior Member     Joined: Jan 2012 Posts: 745 Thanks: 7 How many correct answers did she get? In a mathematics quiz, each correct answer gets 2 marks and a wrong answer attracts -1. Kevwe got a total of 19 in a quiz with 20 questions. How many correct answers did she get? I don’t seem to understand the problem. If she has 19marks and 2 marks is for each correct answer, I will say that she got 9 questions correct which fetched her (9 x 2) marks = 18 marks. I don’t know how the other 1 mark came about that made it 19 marks. By asking how many correct answers she got, I understand it to mean how many questions she answered correctly that gave 19 marks total. Is my understanding correct? if not I need better understanding to this problem.
 June 3rd, 2019, 04:28 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399 basically we're talking about two equations There are 20 total questions, Kevwe gets every question either right or wrong. $r+w=20$ Right answers are +2 points, wrong answers are -1 points. Kevwe scored 19. $2r-w=19$ It's easy enough to solve this, add the two equations. $3r = 39$ $r=13$ $w=20-r = 7$ Kevwe got 13 questions correct, and 7 incorrect. Thanks from Chikis and topsquark
June 4th, 2019, 01:48 AM   #3
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Thanks for the explanation and equation so far. I just want to ask some few questions:
Quote:
 Originally Posted by romsek wrong answers are -1 points.
Does this mean that for every question she answers wrongly, 1 mark will be subtracted from the scores she already have?

Apart from using equation, are there other ways this can be solved?

 June 4th, 2019, 02:41 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,966 Thanks: 2216 Had all 20 questions been answered wrongly, the total marks would have been -20. For each question answered correctly, 2 marks are awarded and one negative mark isn't awarded, making a total improvement of 3 marks. As she got a total of 19 marks, and 19 - (-20) = 39, she got 39/3 = 13 questions correct. Thanks from Chikis
June 4th, 2019, 05:49 AM   #5
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Quote:
 Originally Posted by skipjack Had all 20 questions been answered wrongly, the total marks would have been -20.
What about when all the questions are answered correctly? Would it be 20 × (+2) i.e. 40 marks?

Quote:
 For each question answered correctly, 2 marks are awarded and one negative mark isn't awarded, making a total improvement of 3 marks. As she got a total of 19 marks, and 19 - (-20) = 39, she got 39/3 = 13 questions correct.
How? If she got 13 questions correct, is it not +2 × 13 = 36 marks, which is contrary to the 19 marks?

Last edited by skipjack; June 4th, 2019 at 01:15 PM.

June 4th, 2019, 09:26 AM   #6
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Quote:
 Originally Posted by Chikis What about when all the questions are answered correctly? Would it be 20 × (+2) i.e. 40 marks? How? If she got 13 questions correct, is it not +2 × 13 = 36 marks, which is contrary to the 19 marks?
13 correct, 7 incorrect

13×2 - 7 = 26 - 7 = 19

2 × 13 = 26, not 36

Last edited by skipjack; June 4th, 2019 at 01:16 PM.

 June 4th, 2019, 10:21 AM #7 Senior Member     Joined: Jan 2012 Posts: 745 Thanks: 7 Suppose she had all the 20 questions correct what would be her score?
June 4th, 2019, 11:47 AM   #8
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Quote:
 Originally Posted by Chikis Suppose she had all the 20 questions correct what would be her score?
Are you fooling around? Or you can't multiply 20 times 2 ?

June 4th, 2019, 01:22 PM   #9
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Quote:
 Originally Posted by Chikis What about when all the questions are answered correctly? Would it be 20 × (+2) i.e. 40 marks?
Yes. Each wrong answer would reduce that total by 2 + 1 = 3,
so the number of wrong answers was (40 - 19)/3 = 7,
which means the number of correct answers was 20 - 7 = 13.

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