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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