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inequalities

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inequalities

by vscid » Wed Apr 14, 2010 5:34 pm
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)
The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.
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by 4GMAT_Mumbai » Wed Apr 14, 2010 6:07 pm
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.
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