sinsofgmat wrote:
Is |x-1| < 1?
a> (x-1)^2 <= 2
b> x^2 - 1 > 0
Number line approach:
|a-b| = the distance between a and b on the number line.
Thus:
|x-1| = the distance between x and 1 on the number line.
Draw a number line:
<-----0-----1-----2----->
The question stem asks whether the distance between x and 1 is less than 1.
In order for x to be less than 1 place away from 1, x must within the range in red.
In other words, x must be between 0 and 2.
Question stem, rephrased:
Is 0 < x < 2?
Both statements are satisfied if x=1.1:
Statement 1: (1.1 - 1)² ≤ 2
Statement 2: (1.1)² - 1 > 0
In this case, x is between 0 and 2.
Both statements are satisfied if x=2:
Statement 1: (2 - 1)² < 2
Statement 2: 2² - 1 > 0
In this case, x is NOT between 0 and 2.
Thus, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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
