IgnitedMind wrote:

Is | x | < 1 ?

1) | x + 1 | = 2| x -1 |

2) | x - 3 | not equal to 0

There's another way to deal with absolute (in)equalities.

(i) | x + 1 | = 2| x -1 |

square on both sidesx²+1+2x = 4 ( x² + 1 -2x)

3x²-10x+3=0

(3x-1)(x-3) = 0

so x can be 1/3 or 3 so (i) is insufficient

(ii) |x-3| is not 0, in other words x is not 3 . This is insufficient because x can be one of billions and billions of numbers except 3. so (ii) is not sufficient.

combining (i) and (ii)

(i) says x can be 1/3 or 3

(ii) says x cannot be 3

so i and ii combined say x=1/3. So answer is C

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