|a-b| = the DISTANCE between a and b.fambrini wrote:If y = |x - 2| + |x - 3|, is y = 1?
1) 2 < x < 3
2) x > 2
OA: A
Thus:
|x-2| = the distance between x and 2.
|x-3| = the distance between x and 3.
y = the SUM of these two distances.
Question stem rephrased:
Is the sum of the two distances equal to 1?
The distance between 2 and 3 is 1.
Thus, if x is BETWEEN these two endpoints, then the sum of the two distances will be EQUAL TO 1:
2 <--- |x-2| ---> x <---|x-3|---> 3.
As indicated by the blue portion, |x-2| + |x-3| = the distance between 2 and 3 = 1.
By extension, if x is BEYOND either endpoint -- if x is to the left of 2 or to the right of 3 -- then the sum of the two distances will be GREATER THAN 1.
Thus:
y=1 if x is between 2 and 3.
y>1 if x if x<2 or x>3.
Statement 1: 2<x<3
Since x is between 2 and 3, y=1.
SUFFICIENT.
Statement 2: x>2
If x=2.5, then x is between 2 and 3, with the result that y=1.
If x=4, then x is NOT between 2 and 3, with the result that y>1.
INSUFFICIENT.
The correct answer is A.
