GmatKiss wrote:moonraker wrote:The answer should be C
Could you pls explain the same.
TIA,
GK
The only possible quadrants for (a,b) would be 1st and 3rd as the sign of the both a and b would be same. hence (-a,b) and (-b,a) would be in the same quadrant which would again either be 2nd or 3rd.
For example, 1,2 or -1,-2 .
now for (-a,b) the co-ordinates would be (-1,2) and for (-b,a) it would be (-2,1) which both lie in quadrant number 2.
For (-1,-2) :
Taking (-a,b) the co-ordinates would be (1,-2) and for (-b,a) it would be (2,-1) which lie in quadrant number 4.
Note: Try taking the co-ordinates from quadrant 2 and 4 for (a,b)------- you will not find the conditions of the co-ordinates lying in the same quadrant to be true.
So we now know that (a,b) will lie in quadrant number 1 or 3....................
Now for (-x,y) lying in the same quadrant as (-a,b) or (-b,a)....... which are Q1 and Q3.
Statement 1: xy > 0........ this is only possible when (x,y) lie in Q1 or Q3.
here we do not know which quadrant exactly and also we don't know where do (a,b) and (-a,b) or (-b,a) lie.
Statement 2: ax > 0...........
this tells us that both a and x will lie in the same quadrant i.e: Q1 or Q3 but always same quadrant.
Statement 1 and 2 individually do not provide any clear solution.
But combining both of them we see that (a,b) and (x,y) will always lie in the same quadrant........
hence (-a,b) and (-x,y) will also lie in the same quadrant along with (-b,a)(Q1 or Q3)..........
here the specific quadrant itself does not matter........but being in the same quadrant is all what matters
=> hence option C....
