Adam scores a total of 24 marks.
There are a total of 21 questions.
Every correct answer will earn 4 marks.
Every blank answer will earn 0 mark.
Every wrong answer will have 2 marks deducted.
If Adam gets more than 4 wrong questions,
How many questions are (a) incorrectly answered, (b) correctly answered and (c) left blank?
Number of correct answers |
Scores earned |
Number of incorrect answers |
Scores deducted |
Number of blank answers |
Total score |
21 |
21 x 4 = 84 |
0 |
0 |
0 |
84 |
20 |
20 x 4 = 80 |
1 |
1 x 2 = 2 |
0 |
78 |
10 |
10 x 4 = 40 |
10 |
10 x 2 = 20 |
1 |
20 (x) |
10 |
10 x 4 = 40 |
8 |
8 x 2 = 16 |
3 |
24 (✓) |
If Adam answers all questions correctly, the total score would be 21 x 4 = 84
Assuming there are no blank questions (all questions are either correct or wrong),
Difference between maximum score and Adam's score = 84 - 24 = 60
Difference for every increase in incorrect answer (assuming there is no blank answer)
= 84 - 78
= 6
Thus, estimated number of incorrect questions
= 60 ÷ 6
= 10 r 0
If Adam answers 10 correct answers, 10 incorrect answers and leaves 1 questions blank,
the total score is 20.
Since 20 is less than 24, we need to reduce the number of incorrect answers and increase the number of blank answers to increase the total score.
Through guess and check
(a) Number of questions incorrectly answered = 10
(b) Number of questions correctly answered = 8
(c) Number of questions left blank = 3
Answer(s): (a) 10; (b) 8; (c) 3