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Source: — Data Sufficiency |

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by lunarpower » Fri May 02, 2008 12:47 am
first off, there's a general fact here, waiting to be digested:

if you take a number, square it, and then square-root the result, you get the absolute value of the original number. in other words, √(x^2) = |x|.

just think about plugging two opposite numbers, say -5 and 5, into the expression √(x^2) and this fact should become abundantly clear to you.

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so here's what's going on in this question: is the absolute value of x - 3 equal to 3 - x?

but check this out: the absolute value of x - 3 is either x - 3 itself or its negative, which is 3 - x. like other absolute values, it will be the expression itself (x - 3) if x - 3 is 0 or greater, and will be 3 - x if x - 3 is 0 or less.

so: the question is
is x - 3 < 0?
or
is x < 3?

so (1) is insufficient.

(2) is just a fancy schmancy way of saying that x is negative. if you don't see this right away, then realize that both of the mathematical constructs found in that statement - the negative sign and the absolute value - only discriminate between positive/negative/zero, so that's all you have to think about. (by contrast, if you see a comparison of powers, such as x^2 < x, then you also have to think about whether x is greater or less than 1.)
but if x is negative, then we know that it's less than 3; hence this one is sufficient.

answer = b
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