Is sqrt( (x-5)^2) = 5 - x?
1) -x |x| > 0
2) 5 - x > 0
Please help..I am having trouble unwinding the stem..
Thank you..
OA
d
Absolute values!!!
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Target question: Is sqrt( (x-5)^2) = 5 - x?viveksingh222 wrote:Is sqrt( (x-5)^2) = 5 - x?
1) -x |x| > 0
2) 5 - x > 0
As you suggested, this is a great candidate for rephrasing the target question.
There's a useful rule that says: sqrt(n^2) = |n|
If we apply it here, we can rephrase the target question . . .
Rephrased target question: Is |x-5| = 5-x?
IMPORTANT |x-5| is always greater than or equal to 0. So, in order for |x-5| to equal 5-x, it must be the case that 5-x is greater than or equal to 0. In other words, if 5-x is greater than or equal to 0, then we can be certain that |x-5| = 5-x.
So, we can rephrase the target question one last time.
Rephrased target question: Is 5-x > 0
Once we've simplified the target question, the statements are a breeze.
Statement 1: -x |x| > 0
Since |x| > 0, and since neither (-x) nor |x| can equal zero, we can conclude that (-x)(positive number) > 0
So, (-x) must be positive, which means x must be negative.
If x is negative, then 5-x > 0
Since we can answer the rephrased target question with certainty, statement 1 is SUFFICIENT
Statement 2: 5 - x > 0
Perfect!
If 5 - x > 0 then 5-x > 0
Since we can answer the rephrased target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
Aside: If anyone is interested, we have a free video on rephrasing the target question https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
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It helps to know the following:is root(x-5)^2 = 5-x?
1. -x|x| >0
2. 5-x >0
√ means the POSITIVE ROOT ONLY.
Thus, √(x²) = |x|.
|x-y| = the DISTANCE between x and y.
In the problem at hand:
√(x-5)² = |x-5| = the DISTANCE between x and 5.
A distance must be greater than or equal to 0.
5-x = the DIFFERENCE between 5 and x.
A difference can be negative, 0, or positive.
The DIFFERENCE between two values is equal to the DISTANCE between the two values whenever the DIFFERENCE is greater than or equal to 0.
Thus, |x-5| = 5-x whenever 5-x≥0.
Question rephrased: Is x≤5?
Statement 1: -x|x| > 0
Since |x| cannot be negative, both factors (-x and |x|) must be positive.
Thus:
-x > 0
x<0.
Since x<0, we know that x≤5.
SUFFICIENT.
Statement 2: 5-x > 0
Thus, x<5.
SUFFICIENT.
The correct answer is D.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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