Quiz questions
Jack does a 20-question quiz. How many questions didn't he attempt?
Age
11 to 14
Challenge level
Problem
A quiz has twenty questions with 7 points awarded for each correct answer, 2 points deducted for each wrong answer and 0 for each question omitted.
Jack scored 87 points.
How many questions did he omit?
Student Solutions
Answer: Jack omitted 5 questions.
Jack must have scored at least 87 points from his correct answers.
12 correct $\times$ 7 = 84 points
13 correct $\times$ 7 = 91 points
91 points $-$ (2 wrong $\times$ 2) = 87 points.
So Jack could have got 13 right, 2 wrong and omitted 5
Could he have got more than 13 correct?
14 correct $\times$ 7 = 98 points
98 points $-$ (number wrong $\times$ 2) cannot be 87
15 correct $\times$ 7 = 105 points
105 points $-$ (9 wrong $\times$ 2) = 87 points.
But 15 right and 9 wrong is not possible because there are only 20 questions.