A quiz has 25 questions with 7 points awarded for each correct answer two points
deducted for each wrong answer and zero-point given for each question omitted.
Sakshee scores 113 points totally so how many questions did she omit?
Answers
Let each correct answer be represented by x and each wrong answer by y. Hence each correct answer would fetch 7x marks and wrong answer will lose 2y marks. Let omitted questions be z.
Hence x+y+z =20.
A person getting all correct answers will get a maximum of 140 marks. Similarly a person getting all wrong answers would get -40
Hence the equation will be:
7x -2y =87 or 87+2y=7x.
It is seen from what is given that he has scored more than 87 marks for the correct answers and the marks scored should also be an odd number.
By trial, when we take 13 as the number of correct answers for which the score is 13×7 =91 marks which when fitted into the equation is:
91 - 2y =87.
This also means he gets 2 wrong answers for which he gets 4 negative marks ..Balance 5 questions he does not attempt.
Answer; He omits 5 questions
Answer:
Let us assume that x + y + z = 25 where x stands for correct answers y stands for wrong ans and z stands for quest omitted.
We knw that total marks scored by Shakshi is 113 from which we can assume that she has attempted 16 question
Because 113 / 7 marks per questn is 16
So,
X=<16
And
X-2y+z =25
16-2y+z=25
As there is already said in the question 0 marks will be given for each question omitted.
Therefore z = 0
And hence
16-2y+0=25
16-2y=25
-2y=25-16
-2y=9
As the X value says
X=<16 and y is 2 marks deducted as wrong ans therefore y will be even number instead of odd number so near by even number from (2,4,6,8) is 8
So we conclude 2Y= 8 instead of 9
And y=8/2 and i. e., 4
Therefore y=4
So x total questn for correct ans is 16
And total number of question went wrong y=4
Total questions in the quiz was 25. 16 answers were correct 4 answer were wrong and balance left question is 5.
Therefore, 5 is the number of questions she omitted.