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Is xy > 0 ? (1) x – y > –2 (2) x – 2y < –6
The question is based on inequalities.
Answer: (1) x – y > –2 (2) x – 2y < –6, both should hold good for xy > 0.
Let us find the correct option to suit the condition xy > 0.
Explanation:
 if x  y >  2
x = 10, y = 8  x  y = 2 > 2  xy = 10(8) = 80 > 0  possible case  
x = 10, y = 2  x  y = 10  (2) = 12 > 2  xy = 10(2) = 20 < 0  condition fails 

if x – 2y < –6
x = 1, y = 9  x  2y = 1  18 = 17 < 6  xy = 1(9) = 9 > 0  possible case  
x = 1, y = 10  x  2y = 1  2(10) = 1 20 =  21< 6  xy = 1(10) = 10 < 0  condition fails 

if we combine both x  y >  2 and x – 2y <  6
x  y > 2 and second statement : 2y  x > 6
[ x  y > 2 ] + [ 2y  x > 6 ]
x  y + 2y  x > 2 + 6
y > 4
x > 2
xy > 0
Thus, both the conditions should be clubbed to have xy > 0.
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