adi wrote:If a and b are nonzero numbers on the number line, is 0 between a and b?
(1) The distance between 0 and a is greater than the distance between 0 and b.
(2) The sum of the distances between 0 and a and between 0 and b is greater than the distance between 0 and the sum of a + b.
Answer should be "Statement (2) alone is sufficient.
Absolute value means distance from 0.
Statement 1: |a| > |b|
Plug in a=3, b=2.
This works, because |3| > |2|.
Is 0 between 3 and 2? No.
Plug in a= -3, b=2.
This works, because |-3| > |2|.
Is 0 between -3 and 2? Yes.
Since the answer can be both No and Yes, insufficient.
Statement 2: |a| + |b| > |a+b|
Plug in a=3, b=2.
|3| + |2| > |3+2|. Doesn't work, because |3| + |2| = |3+2|.
This shows us that a and b cannot both be positive.
Plug in a = -3, b = -2.
|-3| + |-2| > |-3 + (-2)|. Doesn't work, because |-3| + |-2| = |-3 + (-2)|.
This shows us that a and b cannot both be negative.
Since a and b cannot both be positive -- nor can they both be negative -- 0 must be between them. Sufficient.
The correct answer is
B.
For example:
Plug in a=-3, b=2.
This works, because |-3| + |2| > |-3+2|.
Is 0 between -3 and 2? Yes.
Plug in a=3, b=-2.
This works, becuase |3| + |-2| > |3+(-2)|.
Is 0 between 3 and -2? Yes.
Since the answer is consistently Yes, sufficient.
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