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
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.
