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June 3rd, 2019, 04:19 PM   #1
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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.
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June 3rd, 2019, 04:28 PM   #2
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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.
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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 View Post
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?
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June 4th, 2019, 02:41 AM   #4
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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.
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June 4th, 2019, 05:49 AM   #5
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Quote:
Originally Posted by skipjack View Post
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.
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June 4th, 2019, 09:26 AM   #6
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Quote:
Originally Posted by Chikis View Post
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.
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June 4th, 2019, 10:21 AM   #7
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Suppose she had all the 20 questions correct what would be her score?
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June 4th, 2019, 11:47 AM   #8
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Quote:
Originally Posted by Chikis View Post
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 ?
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June 4th, 2019, 01:22 PM   #9
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Quote:
Originally Posted by Chikis View Post
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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