Problem 12 · 2014 Math Kangaroo
Medium
Counting & Probability
careful-countingcasework
Katja throws darts at the target shown on the right. If she does not hit the target she gets no points. She throws twice and adds her points. What can her total not be?
Show answer
Answer: D — 90
Show hints
Hint 1 of 3
Each single throw can only score one of the numbers on the target (or 0 for a miss).
Still stuck? Show hint 2 →
Hint 2 of 3
Try adding two of those numbers together in every way you can.
Still stuck? Show hint 3 →
Hint 3 of 3
Check each answer choice to find the one total you can never build.
Show solution
Approach: add the two throws in every way and find the missing total
- One throw scores 0, 30, 50 or 70, and the total is two throws added.
- Make each choice: 60 = 30 + 30, 70 = 0 + 70, 80 = 30 + 50, 100 = 30 + 70 (or 50 + 50).
- No two of the scores add up to 90, so 90 is the total she can never get.
- Answer: 90.
Mark:
· log in to save