In which quadrant of the coordinate plane does the point (x, y) lie?
(1) |xy| + x|y| + |x|y + xy > 0
(2) -x < -y < |y|
(1) |xy| + x|y| + |x|y + xy > 0
(2) -x < -y < |y|
I use to use this question in my drill sets...lol
Statement (1): Consider x and y have the same signs
x = 2, y= 2
4 + 4 + 4 +4 > 0 True
Consider x is neg y is pos
x = -2 y = 2
4 + (-4) + 4 + (-4) >0 is false
consider x is pos y is neg
x = 2 y = -2
4 + 4 + (-4) + (-4) > 0 is false
consider both x and y are negative
x = -2 y = -2
4 + (-4) + (-4) + 4 > 0 is false
Therefore, that statement is only true when x and y are positive. That means that x and y lie in Quandrant 1. Statement(1) sufficient.
Do the same thing with statement (2)
x = 2 y = 1
-2 < -1 < 1 is true
x = -2 y =1
- (-2) < -1 < 1 is false
x = 2 y - -1
-2 < 1< 1 is false
x = -2 y =-1
- (-2) < -(-1) < 1 is false
Once again the only combination that worked was when x and y were both positive. Therefore choose D
