Question 1159363: A quiz has twenty questions with seven points awarded for each correct answer, two points deducted for each wrong answer and zero for each questions omitted. Jack scores 87 points. How many questions did he omit?
Answer by greenestamps(13195)   (Show Source):
You can put this solution on YOUR website!
He gets 7 points for each correct answer, and 2 points are deducted for each wrong answer. So his score is some multiple of 2 less than some multiple of 7.
So look for a way to make a total of 87 by subtracting a multiple of 2 from a multiple of 7.
The smallest multiple of 7 greater than 87 is 91, representing 91/7 = 13 correct answers.
To get a score of 87 with 13 correct answers, the number of wrong answers had to be (91-87)/2 = 4/2 = 2.
With 13 correct answers and 2 wrong answers, the number of questions omitted on the 20 question test was 5.
It should be easy to see, by looking at multiples of 7 greater than 91, that there is no other way for him to get a score of 87.
ANSWER: He omitted 5 questions.
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