kevincanspain wrote:If x and y are integers such that x(y + 4) > 0 , what is the value of x?

(1) (x - 2)(y + 3) < 0
(2) (x - 1)(y + 2) = 0

As x(y + 4) > 0, either {x > 0 and (y + 4) > 0} or {x < 0 and (y + 4) < 0}
So, either {x > 0 and y > -4} or {x < 0 and y < -4}
Hence, value of x will depend upon the the nature of y.
If y > -4, x will be positive
And if y < -4, x will be negative.

Statement 1: Either {(x - 2) > 0 and (y + 3) < 0} or {(x - 2) < 0 and (y + 3) > 0}

• Case #1 : (x - 2) > 0 and (y + 3) < 0
  • So, x > 2 and y < -3
    Now, if -4 < y < -3, y cannot be an integer ---> Not possible
    And, if y < -4 < -3, x must be negative, but we started with x > 2.
    So, there is no possible value of x in this case.
  Case #2 : (x - 2) < 0 and (y + 3) > 0
  • So, x < 2 and y > -3
    Now, if -4 < -3 < y, x must be positive but less than 2 ---> As x must be an integer, only possible value of x is 1.
    And, it is not possible that y < -4 and y > -3.
    So, there is only one possible value of x.

Sufficient

Statement 2: Either (x - 1) = 0 or (y + 2) = 0

• Case #1 : (x - 1) = 0
  • So, x = 1
  Case #2 : (y + 2) = 0
  • So, y = -2
    --> y > -4
    --> x is positive

x can be any positive integer depending upon whether y = -2 or not.

Not sufficient

The correct answer is A.

hutch27 wrote:I'm very confused about this question. What did you use to come up with (for the question) either x>0 and y>-4 or x<0 and y<-4? I guess I have the same question about statement 1 too. I don't get this question at all.

In the question stem it is given that x(y + 4) > 0
This means the product of x and (y + 4) is positive.
Now product of two integers is positive only if either both of them are positive or both of them are negative.

In this case either x and (y + 4) both positive or x and (y + 4) both negative. In mathematical language, either x > 0 and (y + 4) > 0 or x < 0 and (y + 4) < 0 ---> either x > 0 and y > -4 or x < 0 and y < -4

Hope that helps.