Problem 7 · 2020 Math Kangaroo
Easy
Arithmetic & Operations
Number Theory
casework
Carlos wants to square the sum of three numbers chosen from the list −5, −3, −1, 0, 2, 7. What is the smallest result he can get?
Show answer
Answer: B — 1
Show hints
Hint 1 of 2
A square is never negative, so you want the sum of the three numbers to be as close to 0 as possible.
Still stuck? Show hint 2 →
Hint 2 of 2
Can three of the listed numbers add to exactly 0? If not, the next best is a sum of ±1.
Show solution
Approach: make the sum nearest to zero
- Squaring makes any sum non-negative, so aim for a sum near 0.
- No three of −5, −3, −1, 0, 2, 7 add to exactly 0.
- But −3 + 0 + 2 = −1 gives a sum of magnitude 1.
- Then the square is 1² = 1, the smallest result, choice B.
Mark:
· log in to save