Is sqrt ((x-3)^2) = 3-x?
(1) x not equal to 3
(2) -x|x| > 0
Don't know how to go about this ... How to arrive at the answer?[/spoiler]
DS: Difficulty level: 700, Source: GMATPrep
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The square root of a square is a coded way of saying absolute value. Whether the base is positive or negative, squaring will make it positive, and when given a root sign, we only take the positive root:
So, we can rephrase the question this way:
|x - 3| would equal (x - 3) if (x - 3) is greater than or equal to zero. It would equal 3 - x (in other words, -1(x - 3)) if x - 3 is negative.
So the question becomes:
x - 3 < 0 ? -->
x < 3 ?
(1) x not equal to 3
This does not answer our target question. x could still be greater than 3 (giving us a "no" answer to the question) or less than 3 (giving us a "yes" answer to the question). Insufficient.
(2) -x|x| > 0
Since |x| is always positive (for any non-zero x), then the only way to get a positive product of -x and |x| is if -x is positive as well.
If -x is positive, then x must be negative. Since our target question is "is x < 3 ?", then any negative value for x would give us a definitive "yes" answer to the question.
The answer is B.
So, we can rephrase the question this way:
|x - 3| would equal (x - 3) if (x - 3) is greater than or equal to zero. It would equal 3 - x (in other words, -1(x - 3)) if x - 3 is negative.
So the question becomes:
x - 3 < 0 ? -->
x < 3 ?
(1) x not equal to 3
This does not answer our target question. x could still be greater than 3 (giving us a "no" answer to the question) or less than 3 (giving us a "yes" answer to the question). Insufficient.
(2) -x|x| > 0
Since |x| is always positive (for any non-zero x), then the only way to get a positive product of -x and |x| is if -x is positive as well.
If -x is positive, then x must be negative. Since our target question is "is x < 3 ?", then any negative value for x would give us a definitive "yes" answer to the question.
The answer is B.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education