Which of the following represents the range for all X which satisfy |1 - X| < 1 ?
(-1, 1)
(-1, 2)
(0, 1)
(0, 2)
(1, 2)
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inequalities
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4GMAT_Mumbai
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IMO, the answer is D
Logical way:
Mod (1-X) refers to the magnitude of the difference between 1 and X on the number line. If distance between 1 and X should be less than 1; then X should lie at a point less than a unit distance from 1. That would boil down to [spoiler](0,2)[/spoiler]
Arithmetic way:
Mod (1-x) < 1
is equivalent to -1 < 1-X < 1
Subtract 1 across the board (to get rid of the 1 just before X)
-2 < -X < 0
Multiply by -1 across the board (to get rid of the -ve sign of X)
[spoiler]2 > X > 0; which is equivalent to 0 < X < 2[/spoiler].
Hope this helps.
Logical way:
Mod (1-X) refers to the magnitude of the difference between 1 and X on the number line. If distance between 1 and X should be less than 1; then X should lie at a point less than a unit distance from 1. That would boil down to [spoiler](0,2)[/spoiler]
Arithmetic way:
Mod (1-x) < 1
is equivalent to -1 < 1-X < 1
Subtract 1 across the board (to get rid of the 1 just before X)
-2 < -X < 0
Multiply by -1 across the board (to get rid of the -ve sign of X)
[spoiler]2 > X > 0; which is equivalent to 0 < X < 2[/spoiler].
Hope this helps.
