Is x>1?
(1) (x+1)(|x|-1)>0
(2) |x|<5
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Is x>1?
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srcc25anu
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St1: For x > 1, lets say x = 2 (x+1)(|x|-1) = 3*1 = 3 > 0
For -1 < x < 1, lets say x = 0 (x+1)(|x|-1) = 1*-1 = -1 < 0
For x < -1, lets say x = -2 (x+1)(|x|-1) = (-1)*1 = -1 < 0
Hence only valid range when (x+1)(|x|-1)>0 is when x > 1
Sufficient
St2: |x| < 5 implies -5 < x < 5
-4 is < 1 but 4 > 1
hence insufficient
Ans A
For -1 < x < 1, lets say x = 0 (x+1)(|x|-1) = 1*-1 = -1 < 0
For x < -1, lets say x = -2 (x+1)(|x|-1) = (-1)*1 = -1 < 0
Hence only valid range when (x+1)(|x|-1)>0 is when x > 1
Sufficient
St2: |x| < 5 implies -5 < x < 5
-4 is < 1 but 4 > 1
hence insufficient
Ans A
