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 ? 

Concept:

For the sum of four numbers to be even, you either need to have

• All four numbers be even
• All four numbers be odd
• Two of them be even and two of them be odd

Explanation:

a + b + c + d = 200   (even)

As discussed above

Case:1 All four numbers be even

S = 1 + 1 + 1 + 1 = 4

Case:2 All four numbers be odd

S  = - 1 - 1 - 1 - 1 = - 4

Case:3 Two of them be even and two of them be odd

S = 1 + 1 - 1 - 1 = 0

∴ There will be three possible values of S.