Damn it! Exam! - Part 2

Algebra Level 2

Mehul had a Social Studies exam which was worth 20 marks.There were 10 questions worth 2 marks each.But there was negative marking scheme such that if Mehul gets a question correct then he will get 2 marks , but if he gets it wrong , he will get -0.5 marks.If Mehul scored 75% in the test and he attempted all the questions, Find the number of questions he got correct.

This problem is created by me!


The answer is 8.

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Nihar Mahajan by Nihar Mahajan , 20, India

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4 solutions

Nihar Mahajan
May 13, 2015

Let the number of questions Mehul got correct be ' x x ' and since the total questions are 10 10 , the ones he got wrong will be ( 10 − x ) (10-x) .

Hence , the marks he got due to correct attempt = 2 ( x ) = 2(x)

Hence , the marks he got due to wrong attempt = − 0.5 ( 10 − x ) = -0.5(10-x)

Since he got 75 % 75\% , we can write equation:

2 x − 0.5 ( 10 − x ) = 75 100 × 20 2 x − 5 + 0.5 x = 15 2.5 x = 20 25 x = 200 x = 200 25 x = 8 2x-0.5(10-x)=\dfrac{75}{100} \times 20 \\ 2x-5+0.5x=15 \\ 2.5x=20 \\ 25x=200 \\ x=\dfrac{200}{25} \\ \boxed{x=8}

Hence , Mehul got 8 8 questions correct. Cheers!

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Cheers, Mate!

Mehul Arora - 6 years, 1 month ago

Please add that Mehul attempts all the questions. Although he cannot anyway answer only 75 % 75 \% of the questions but for the sake of clarity you must add that.

Sudeep Salgia - 6 years, 1 month ago

Part 3 :P

Rohit Ner - 6 years, 1 month ago

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But I didn't have social studies exam :/

Nihar Mahajan - 6 years, 1 month ago

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Hehe who cares. There are a no. of Nihars on this planet. :P . Hope you like it. :) Cheers!

Rohit Ner - 6 years, 1 month ago

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@Rohit Ner – BTW nice problem. :)

Nihar Mahajan - 6 years, 1 month ago

Mehul posted solution for his Part 1.

I posted solution for my Part 2.

So , @Rohit Ner now , you post a solution for Part 3 :P :P :P xD Cheers!

Nihar Mahajan - 6 years, 1 month ago
Tsuna Quintil
Sep 28, 2015

Perfect score = 100% --> Mehul's score= 75%

Which means he got 25% of the exam wrong --> For every wrong, he will get -0.5 marks --> In order for us to get 25% from the -0.5 marks we need to multiply -0.5 by itself --> -0.5*-0.5 = 1/4 ---> 25% --> 10-2 = 8

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Happy Jiawei
Aug 8, 2015

Non-algebraic solution:

Assume all answered correctly --> 20 marks

For each question answered wrongly, 2 + 0.5 = 2.5 forfeited from perfect score.

100 - 75 = 25%

25/100 x 20 = 5 marks forfeited in total

5 / 2.5 = 2 questions answered wrongly.

10 - 2 = 8 questions answered correctly.

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Desai Paritosh
Jun 1, 2015

let x be the number of Mehul got correct and y be the number of answers that Mehul got incorrect

75% of 20 is 15 , thus Mehul got 15 marks

thus (2)x - (0.5)y=15...............................................{1}

by multiplying eq {1} by 2 we get,

[4]x-y=30............................................................{2}

he attempted all question thus,

x+y=10..................................................{3}

by adding eq {2} and eq {3} we get

[5]x=40

x=8

thus, Mehul got 8 questions correct

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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