Solving the Test Paper Marks Problem
This problem involves calculating the number of correct answers based on the total questions attempted, the marks awarded for correct answers, the penalty for wrong answers, and the final score.
Set Up the Variables
- Let $ c $ represent the number of questions answered correctly.
- Let $ w $ represent the number of questions answered incorrectly.
Formulate Equations
From the question, we have two key pieces of information:
- The total number of questions attempted is 76: $ c + w = 76 $
- The total marks obtained is 144, with +3 for correct and -1 for wrong: $ 3c - w = 144 $
Alternative Solution Method (Exam Focused)
- Assume all attempts were correct: If all 76 questions were answered correctly, the total marks would be $ 76 \times 3 = 228 $ marks.
- Calculate the difference in marks: The student scored 144 marks, which is $ 228 - 144 = 84 $ marks less than the maximum possible score assuming all were correct.
- Determine the mark difference per wrong answer: Each wrong answer costs 1 mark (penalty) and loses the 3 marks that would have been awarded if correct. So, each wrong answer results in a total difference of $ 3 + 1 = 4 $ marks compared to a correct answer.
- Calculate the number of wrong answers: Divide the total mark difference by the difference per wrong answer: $ \frac{84}{4} = 21 $ wrong answers.
- Calculate the number of correct answers: Subtract the number of wrong answers from the total questions attempted: $ 76 - 21 = 55 $ correct answers.
Verification
Check the result: $ 55 $ correct answers and $ 21 $ wrong answers.
- Total Questions: $ 55 + 21 = 76 $ (Correct)
- Total Marks: $ (55 \times 3) - (21 \times 1) = 165 - 21 = 144 $ (Correct)
Therefore, the student answered 55 questions correctly.
Similar Questions
- Read the given paragraph and answer the question.
There are five persons A, G, M, J and D. Every person has to select one item each from a box containing items numbered from 1 to 5. A and J selected items 5 and 2 respectively. G cannot select item 3, while M cannot select item 3 or 5.
Which item can G select? - Read the given information carefully and answer the question that follows.
- There are four persons: P, Q, R and S.
- One of them is a doctor and plays football and cricket.
- P and Q are teachers.
- P plays badminton.
- The lawyer and both the teachers are swimmers.
- One of them also plays tennis.
- S plays carrom and is a lawyer.
- All the four persons play two games each and follow one profession.
The rectangle represents a set of calculations that are common across all the given equations. Identify the calculations involved and solve the fourth equation on the same basis:
$7 \blacksquare 4 = 27/4$
$6 \blacksquare 1 = 5$
$4 \blacksquare 3 = 11/3$
$a \blacksquare b = ?$- Four girls, Radha, Neena, Mohita and Jyoti, are to be served in a sequence by a service provider. However, there are some limitations as follows: Mohita and Jyoti cannot be served one after the other; Neena cannot be served at the third number in sequence; and Radha and Neena are to be served one after the other. Considering the given information, which of the following statements is compulsorily true?
- In a school there were 6 teachers. A and B taught Hindi and English. D and A taught Mathematics and Science. C and E taught English and Mathematics. F and B taught Hindi and French. Who taught the maximum number of subjects?
- Five children A, B, C, D and E ate mangoes. A ate 8 mangoes less than B. C and E together ate 37 mangoes. D ate 8 mangoes more than C. B ate 5 mangoes more than C. B and A together ate 40 mangoes. Considering the above information, which of the following statements is correct?
- Huma's mother gave Huma 4 baskets of blueberries each labelled A, B, C, D. Each berry weighs 5 g, except for the basket, which has all rotten berries, where each berry has a weight of 3 g. Huma took out 1, 2, 3 and 4 berries from the baskets A, B, C and D respectively and weighed them to be 44 grams. Which basket has the rotten berries?
- In a test series, South Africa defeated England twice, Bangladesh defeated South Africa twice, England defeated Bangladesh twice, South Africa defeated Pakistan twice and Bangladesh defeated Pakistan twice. Which country lost the highest number of times?
Important Questions from Problem Solving
Evaluate 5793405 x 99999
A tight fitting band is wrapped around the Equator. Another circular band whose length is 15 m more lies at a certain height over the first band. A group of human beings attempt to pass under the longer band. Can they walk under it?
(Earth’s circumference is roughly 40000 km. The height of human beings is between 1 & 2m)
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(84, 73, 157) (96, 88, 184)
- Arrange the problem-solving strategy.
(A) Generate many possible solutions
(B) Determine how to implement the solution and evaluate the success of the solution
(C) Make a decision
(D) Evaluate each solution
(E) Define the problem
Choose the correct answer from the options given below. People who are closest to information technology agree with the observation that benefits of screens as a learning tool are overblown and the risks for addiction and stunting development seems high. Screens are said to be beyond personal control and we situate them in pleasure centres of the developing brains. As a responsible parent you will
