In a test there were 25 multiple-choice questions. They were marked as follows:
2 marks for each correct answer
0 marks for a non-attempt
1 mark for an incorrect answer.
Sarah attempted
4
5 of the questions and received 22 marks. How many questions did
she answer correctly?
Again we can set this up as two simultaneous equations
2 marks for each correct answer A
0 marks for a non-attempt (not interested in these)
1 mark for an incorrect answer B
A+B=20 (she only answered 4/5 of 25 questions)
2A+B=22 based on the marks
solve the two for A
To find out how many questions Sarah answered correctly, we need to compare the total marks she received with the marks she would have received if all her attempted questions were correct.
First, let's calculate the total marks Sarah would have received if all her attempted questions were correct. Since each correct answer is worth 2 marks and Sarah attempted 4 + 5 = 9 questions:
Marks for correct answers = 2 x number of correct answers
= 2 x 9
= 18 marks
Now, let's calculate the total marks she actually received, which is given as 22 marks.
Since each incorrect answer is worth 1 mark, the difference between the total marks she received and the total marks she would have received if all her answers were correct represents the number of incorrect answers.
Difference in marks = Total marks she received - Total marks for correct answers
= 22 - 18
= 4 marks
Therefore, Sarah received 4 incorrect answers. To find out how many questions she answered correctly, we subtract the number of incorrect answers from the total number of attempted questions:
Number of correct answers = Total number of attempted questions - Number of incorrect answers
= 9 - 4
= 5
Hence, Sarah answered 5 questions correctly.