If |a-b| = |b-c| = 2, what is |a-c|?
1. a<b<c
2. c-a < c-b
|x-y| = the DISTANCE BETWEEN x and y.
|a-b| = |b-c| = 2, in words:
The distance between a and b is 2.
The distance between b and c is 2.
Question stem, in words:
What is the distance between a and c?
Plot the distances on a NUMBER LINE.-
Statement 1: a<b<c.
Since b is BETWEEN a and c, the number line must look like this:
a<----2---->b<----2---->c.
Thus, the distance between a and c is 4.
SUFFICIENT.
Statement 2: c-a < c-b
-a < -b
a>b.
The number line could look like this:
c<----2---->b<----2---->a.
In this case, the distance between a and c is 4.
If a=c, the number line could look like this:
b<----2---->a=c.
In this, case, the distance between a and c is 0.
INSUFFICIENT.
The correct answer is
A.
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