Bunuel wrote:
7. |x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2
This one is quite interesting.
First note that |x+2|=|y+2| can take only two possible forms:
A. x+2=y+2 --> x=y. This will occur if and only x and y are both >= than -2 OR both <= than -2. In that case x=y. Which means that their product will always be positive or zero when x=y=0.
B. x+2=-y-2 --> x+y=-4. This will occur when either x or y is less then -2 and the other is more than -2.
When we have scenario A, xy will be nonnegative only. Hence if xy is negative we have scenario B and x+y=-4. Also note that vise-versa is not right. Meaning that we can have scenario B and xy may be positive as well as negative.
(1) xy<0 --> We have scenario B, hence x+y=-4. Sufficient.
(2) x>2 and y<2, x is not equal to y, we don't have scenario A, hence we have scenario B, hence x+y=-4. Sufficient.
Answer: D.
Hi
Bunuel,
I tried using the number line to simulate A scenario and could get it something like below and this somehow looks fine.
--y/x-------- (-2)-----------
----------(-2)-------------x/y
I am not able to understand B scenario from the number line as we can have any distance between x and y. its just that the distance of x from -2 and y from -2 should be same and in opposite sides. How does the -4 come into the picture here ?
-------x<----------d------->(-2)<---------d-------->y---------
now this d here can be anything right ?