2023 · Q31
Let a, b, c and d be four positive integers such that a + b + c + d = 200. If S = (-1)a + (-1)b + (-1)c + (-1)d, then what is the number of possible values of S?
Elementary MathematicsNumber System
- AOne
- BTwo
- CThree
- DFour
Explanation
Each term (−1)^n is ±1, so S lies in {−4, −2, 0, 2, 4}. Since a + b + c + d = 200 is even, the number of odd variables is even (0, 2 or 4), giving S = 4, 0 or −4 respectively. There are three possible values of S (C).