ejager wrote:What is the distance between "a" and "b" on the number line?
1. |a| - |b| = 6
2. ab > 0
Distance between a and b = |a-b|.
Statement 1: |a| = |b| + 6.
Let b=1, implying that |a| = 7.
If a=7, then |a-b| = |7-1| = 6.
If a=-7, then |a-b| = |-7-1| = 8.
Since |a-b| can be different values, INSUFFICIENT.
Statement 2: ab > 0
If a=1 and b=1, then |a-b| = |1-1| = 0.
If a=2 and b=1, then |a-b| = |2-1| = 1.
Since |a-b| can be different values, INSUFFICIENT.
Statements combined:
Both statements are satisfied by a=7 and b=1, in which case |a-b| = |7-1| = 6.
Both statements are satisfied by a=-10 and b=-4, in which case |a-b| = |-10 - (-4)| = 6.
Both statements are satisfied by a=6.5 and b=0.5, in which case |a-b| = |6.5 - 0.5| = 6.
In every case, |a-b| = 6.
SUFFICIENT.
The correct answer is
C.
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