yezz wrote:
If A<Y<Z<B, is |Y-A|< |Y-B|?
(1) |Z-A| < |Z-B|
(2) |Y-A| < |Z-B|
|a-b| = the distance between a and b.
Since a < y < z < b, we get the following number line:
a..........y..........z..........b
Statement 1: |z-a| < |z-b|
Since the distance between y and a is less than the distance between z and a, we get:
|y-a| < |z-a|
Since the distance between z and b is less than the distance between y and b, we get:
|z-b| < |y-b|
Linking the inequalities above to the inequality in Statement 1, we get:
|y-a| < |z-a| < |z-b| < |y-b|
|y-a| < |y-b|
Thus, the answer to the question stem is YES.
SUFFICIENT.
Statement 2: |y-a| < |z-b|
Since the distance between z and b is less than the distance between y and b, we get:
|z-b| < |y-b|
Linking the inequality above to the inequality in Statement 2, we get:
|y-a| < |z-b| < |y-b|
|y-a| < |y-b|
Thus, the answer to the question stem is YES.
SUFFICIENT.
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