number properties

[sud21]

x and y are integers, (1+x)(1+y)=1 y is not 0, which of the following could be the value of x?
-2,-1,0,1,2

[Anurag@Gurome]

x and y are integers, (1+x)(1+y)=1 y is not 0, which of the following could be the value of x?

One obvious approach to solve this question is to plug the options.

• 1. x = -2 --> (1 + x)(1 + y) = -(1 + y) = 1 --> y = -2 --> Possible and we can stop plugging
  In case you don't want to stop...
  2. x = -1 --> (1 + x)(1 + y) = 0 --> NO
  3. x = 0 --> (1 + x)(1 + y) = (1 + y) = 1 --> y = 0 --> NO
  4. x = 1 --> (1 + x)(1 + y) = 2(1 + y) = 1 --> y = -1/2 --> NO
  5. x = 2 --> (1 + x)(1 + y) = 3(1 + y) = 1 --> y = -2/3 --> NO

The correct answer is A.