Problem 3 · 1986 AJHSME
Easy
Arithmetic & Operations
pick-smallest
The smallest sum one could get by adding three different numbers from the set {7, 25, −1, 12, −3} is
Show answer
Answer: C — 3.
Show hints
Hint 1 of 2
To make a sum as *small* as possible, you want each piece you add to be as small as possible. So which three numbers should you grab?
Still stuck? Show hint 2 →
Hint 2 of 2
The smallest possible sum uses the three smallest numbers — and don't be fooled, the most negative numbers are the smallest.
Show solution
Approach: smallest sum = three smallest numbers
- A sum gets smaller every time you swap in a smaller number, so the smallest total comes from the three smallest numbers in the set.
- Order the set: −3, −1, 7, 12, 25. The three smallest are −3, −1, 7, giving −3 + (−1) + 7 = 3.
- Watch the trap: −3 by itself is smaller than 3, but the problem forces you to add *three different* numbers — you can't stop at one or two. The smallest two would be −4, but the required third number drags it back up.
Mark:
· log in to save