kishokbabu wrote:Is √((x-5)^2) = (5-x) ?
1) -x|x| > 0
2) (5-x) > 0
√x² = |x|.
Thus, the question is asking
Is |x-5| = 5-x?
The CRITICAL POINT is x=5: this is where x-5 changes sign.
Case 1: x<5.
When x<5, x-5<0.
Since |x-5| cannot be negative, x-5 must be replaced by 5-x:
5-x = 5-x
0 = 0.
This means that the value of x here is irrelevant: ANY value will work.
Thus, the entire range x<5 satisfies |x-5| = 5-x.
Case 2: x≥5.
In this range, x-5≥0, so the expression does not have to be rewritten.
x-5 = 5-x
2x = 10
x = 5.
This means that the ONLY allowed value in this range is x=5.
Thus, the total range of values that satisfies |x-5| = 5-x is x≤5.
Question rephrased: Is x≤5?
Statement 1: -x|x| > 0.
The expression above is valid only if x<0, so that the expression becomes:
-(negative) * |negative| > 0
positive * positive > 0.
Since x<0, we know that x≤5.
SUFFICIENT.
Statement 2: 5-x > 0.
x<5.
SUFFICIENT.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
