In an objective type test containing 25 questions. A student is to be awarded +5 marks for every correct answer, -5 for every incorrect answer and zero for not writing any answer. Mention the ways of scoring 110 marks by a student.
Solution:
From the above given problem let us write the given data
Total marks scored = 110
Total questions = 25
Marks for correct answer = 5
Marks for incorrect answer = -5
Marks for not writing any answer = 0
If total marks scored is 110 then, minimum correct responses = 110 ÷ (+5) = 22
Let us consider the cases
Case 1
Total correct responses = 22
Total marks for one correct answer = + 5
Marks for 22 correct answers = (22 × 5 = 110)
Marks for incorrect answer = 0
Marks scored = 110
So, in this case no incorrect response is there but, 3 questions were unattempted.
Case 2
Total correct responses = 23
Marks from 23 correct answers = 23 × 5 =115
Total marks scored = 110
Total marks obtained for incorrect answers = 110 - (115) = -5
Total marks for one incorrect answer = -5
Number of incorrect responses = (-5) ÷ (-5) = 1
So in this case, we have 23 correct answers, 1 incorrect answer, and 1 unattempted question.
Case 3
Let us have total correct answers = 24
Marks obtained from 24 correct answers = (24 × 5 = 120)
Total marks scored = 110
Marks obtained for incorrect answers = 110 - 120 = -10
Number of incorrect responses = (-10) ÷ (-5) = 2
Thus the number of questions = 24 + 2 = 26. Whereas, the total number of questions given in the problem is 25. So, this case is not possible to evaluate.
Therefore according to given problem the possible ways are:
a) 22 correct, 0 incorrect, 3 unattempted.
b) 23 correct, 1 incorrect, 1unattempted
✦ Try This: In an objective type test containing 20 questions. A student is to be awarded +4 marks for every correct answer, -4 for every incorrect answer and zero for not writing any answer. Mention the ways of scoring 100 marks by a student
Using the same logic as above, try using the integers rules and substitute the given values case by case to obtain the required possible outcomes
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 1
NCERT Exemplar Class 7 Maths Chapter 1 Solved Ex 16
In an objective type test containing 25 questions. A student is to be awarded +5 marks for every correct answer, -5 for every incorrect answer and zero for not writing any answer. Mention the ways of scoring 110 marks by a student
Summary:
Using the integers properties and further on evaluating the different cases we have the following outcomes: a) 22 correct, 0 incorrect, 3 unattempted b) 23 correct, 1 incorrect, 1unattempted
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