Hi DonZepp and PgRaul,
To start, any time an Absolute Value appears in a Quant question, while there will likely be some solutions to the given equation/inequality that are 'obvious', there will almost certainly be some OTHER solutions that you also have to consider.
With this prompt, we're told that |X - 2| < 5 and we're asked which of the following MUST be true.
The 'obvious' solutions to this inequality are positive integers (re: X = 6, 5, 4, 3 and 2), but there are other solutions, including 1, 0, -1 and -2. Since we're dealing with an inequality, we do have to consider the 'upper limit' and 'lower limit' of the range of solutions, so...
-3 < X < 7
Thus, ANY value of X in that range is a solution for this inequality. Considering THAT 'limitation', which of the following answers is ALWAYS true?
A) X>0.... does X HAVE to be greater than 0? NO... there are a bunch of negative numbers that are solutions.
B) X>8.... does X HAVE to be greater than 8? NO... that's just fundamentally incorrect.
C) X>-4.... does X HAVE to be greater than -4? YES... every possible solution to this inequality IS greater than -4, so this answer IS ALWAYS true. This answer does NOT mean that every number that is greater than -4 is a solution to this inequality. It IS always true based on the set of solutions though (and that's what the question was asking for).
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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