Problem 14 · 2011 Math Kangaroo
Medium
Logic & Word Problems
sum-constraintcasework
A quizshow has the following rules: each contestant begins with 10 points. They must answer 10 questions. For each correct answer they get a point and for each incorrect answer they lose a point. Mrs Blandorfer finished the show with 14 points. How many questions had she answered incorrectly?
Show answer
Answer: D — 3
Show hints
Hint 1 of 3
First imagine she got every single question right and see how many points that would give.
Still stuck? Show hint 2 →
Hint 2 of 3
Compare that perfect score with her real score of 14 points.
Still stuck? Show hint 3 →
Hint 3 of 3
Each wrong answer instead of a right one costs her 2 points: one she does not gain, plus one she loses.
Show solution
Approach: compare with a perfect score
- If all 10 answers were right she would start with 10 and add 10, reaching 20 points.
- She actually finished with 14, which is 20 − 14 = 6 points short of perfect.
- Each wrong answer costs 2 points (she misses the +1 and also loses 1), so 6 ÷ 2 = 3 questions were wrong, answer D.
Mark:
· log in to save