It can also be solved more easily with co-ordinate Geometry approach without any calculation..
|x| + |y| = 32 , it represent a Rombus with vertices on (0,32 ) , (32,0) , (-32,0) and (0,-32) ( Draw the diagram on X / Y axis )
now Question : what is XY ? It will be position in I and III Quardant, and - ive in II and IV Quardant.
Option A --- > it is a equation of line which is symmetric to X and Y axis and it will cut the rombus in II and IV quardant with at points (-x1,y1) and (x1,-y1) , so the product of XY will be same and a -ive value. Sufficient!
Option B --- > this a smaller rombus which does not intersect the bigger Rombus, therefore for all of the possible combination of (X,Y) for |x| - |y| = 16 , we will have
|x| + |y| < 32 .So we dont have any values of (X,Y) . Insufficient.
|x| + |y| = 32 , it represent a Rombus with vertices on (0,32 ) , (32,0) , (-32,0) and (0,-32) ( Draw the diagram on X / Y axis )
now Question : what is XY ? It will be position in I and III Quardant, and - ive in II and IV Quardant.
Option A --- > it is a equation of line which is symmetric to X and Y axis and it will cut the rombus in II and IV quardant with at points (-x1,y1) and (x1,-y1) , so the product of XY will be same and a -ive value. Sufficient!
Option B --- > this a smaller rombus which does not intersect the bigger Rombus, therefore for all of the possible combination of (X,Y) for |x| - |y| = 16 , we will have
|x| + |y| < 32 .So we dont have any values of (X,Y) . Insufficient.