|a| = the DISTANCE between a and 0.Vincen wrote:Is |x|+|x−1|=1 ?
(1) x ≥ 0
(2) x ≤ 1
|a-b| = the DISTANCE between a and b.
Thus:
|x| = the distance between x and 0.
|x-1| = the distance between x and 1.
|x| + |x-1| = (distance between x and 0) + (distance between x and 1).
Question stem rephrased:
Is the sum of the two distances equal to 1?
The distance between 0 and 1 is 1.
Implication:
If x is not beyond either of these two endpoints -- in other words, if x is between 0 and 1, inclusive -- then the sum of the two distances will be EQUAL TO 1:
0 <--- |x| ---> x <---|x-1|---> 1
Here, |x| + |x-1| = the distance between 0 and 1 = 1.
By extension, if x is BEYOND either endpoint -- if x is to the left of 0 or to the right of 1 -- then the sum of the two distances will be GREATER THAN 1.
Question stem, rephrased:
Is x between 0 and 1, inclusive?
Statement 1: x ≥0
If x=1/2, then x is between 0 and 1, inclusive.
If x=2, then x is NOT between 0 and 1, inclusive.
INSUFFICIENT.
Statement 2: x ≤ 1
If x=1/2, then x is between 0 and 1, inclusive.
If x=-1, then x is NOT between 0 and 1, inclusive.
INSUFFICIENT.
Statements combined:
0 ≤ x ≤ 1.
Thus, x is between 0 and 1, inclusive.
SUFFICIENT.
The correct answer is C.
