Examination

In an examination, you have to answer 100 questions and for each wrong answer, there will be a cut 0.4 mark from your actual marks.and your results say you get 65 marks, so how many wrong answers do you have?

Note:we get 1 mark for each right answer.

#NumberTheory

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

Assuming we get 1 mark for each right answer before deduction, and let the number of questions wrongly answered be $x$ . Then we have

$\begin{aligned} (100-x)-0.4x & =65 \\ 1.4x & = 35 \\ \implies x & = 25 \end{aligned}$

Chew-Seong Cheong - 3 years, 8 months ago

@Chew-Seong Cheong Thanks a lot,now I understand it and If we say "we get 2 marks for each right answer" then the result of the number of questions wrongly answered will stay the same?I think the mark for each right answer is not necessary to know to get the amount of wrong answers

Nazmus sakib - 3 years, 8 months ago

200-x-0.4x=65, 135=1.4x. x is not a whole number, meaning that x does matter

Kenny O. - 3 years, 7 months ago

@Kenny O. – For 2 marks for each right answer, 200 is marks not the amount of question.and what do you mean by $x$ ? amount of right answers or amount of wrong answers?

Nazmus sakib - 3 years, 7 months ago

@Kenny O. – It should be $2(100-x)-0.4x = 65$ . Then $x=56/25$

Chew-Seong Cheong - 3 years, 7 months ago

@Chew-Seong Cheong – I mean $x=135/2.4=56.25$

Chew-Seong Cheong - 3 years, 7 months ago

@Chew-Seong Cheong – @Chew-Seong Cheong so is it necessary to know the mark for each right answer to get the amount of wrong answers?

Nazmus sakib - 3 years, 7 months ago

@Nazmus Sakib – No, if it is two marks there is no integer solution. We cannot have 56.25 wrong answers, right? Obviously, the right mark cannot be lower than 0.4. You must understand the equation instead of guessing.

Chew-Seong Cheong - 3 years, 7 months ago

What is the mark for each correct answer?

Munem Shahriar - 3 years, 8 months ago

I've edited that "we get 1 mark for each right answer." although I think the mark for each right answer is not necessary to know to get the amount of wrong answers.

Nazmus sakib - 3 years, 8 months ago

@Calvin Lin @Pi Han Goh @Chew-Seong Cheong

Nazmus sakib - 3 years, 8 months ago

What have you tried? Where are you stuck?

Calvin Lin Staff - 3 years, 8 months ago

I was stuck at the beginning,didn't know how to start.

Nazmus sakib - 3 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$