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das.ashmita
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Target question: Is root[(x-3)^2] = 3-x ?das.ashmita wrote:Is root[(x-3)^2] = 3-x ?
1. x not equal to 3
2. -x|x| > 0
This question is a great candidate for rephrasing the target question.
To begin, notice that we have two nice rules:
- If k > 0, then root(k^2) = k
- If k < 0, then root(k^2) = -k
Now observe that (3-x) = -(x-3)
Given the above information, under what conditions will root[(x-3)^2] = 3-x?
In other words, under what conditions will root[(x-3)^2] = -(x-3)?
This will occur if x-3 is negative.
So, we can now rephrase the target question as: Is (x-3) negative?
Or we can write: Is x-3 < 0?
. . . or better yet: Is x < 3?
Now that we've rephrased the target question in much simpler terms, we can check the statements.
Statement 1: x not equal to 3
This doesn't give us a definitive answer to the rephrased target question (Is x < 3? )
As such, statement 1 is NOT SUFFICIENT
Statement 2: -x|x| > 0
First notice that this implies that x does not equal zero.
Next, notice that, if x does not equal zero, then |x| will always be positive.
So, -x|x| > 0 is the same as saying (-x)(positive) > 0
In other words, the product (-x)(positive) results in a positive number.
This tells us that (-x) must be positive, which means x must be negative.
If x is negative, then x is definitely less than 3.
As such, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
