Note:
|x-y| = |y-x| = the distance between y and x
|x| = |x-0| = the distance between x and 0
RashedVai wrote:
Is |a-c| + |a| = |c|?
(1) ab > bc
(2) ab < 0
Question stem, rephrased:
Is |c-a| + |a-0| = |c-0| ?
In words:
If the distance between c and a is added to the distance between a and 0, is the result equal to the distance between c and 0?
The answer will YES if a is between c and 0, as in the following cases:
c.....a.....0 --> (distance between c and a) + (distance between a and 0) = distance between c and 0
0.....a.....c --> (distance between c and a) + (distance between a and 0) = distance between c and 0
The answer will NO if a is NOT between c and 0, as in the following cases:
a.....c.....0 --> (distance between c and a) + (distance between a and 0) > distance between c and 0
0.....c.....a --> (distance between c and a) + (distance between a and 0) > distance between c and 0
Statement 1: ab>bcIf b=1, a=2 and c=1, then a is NOT between c and 0, so the answer to the question stem is NO.
If b=1, a=-1 and c=-2, then a IS between c and 0, so the answer to the question stem is YES.
INSUFFICIENT.
Statement 2: ab<0No information about c.
INSUFFICIENT.
Statements combined: ab>bc and ab<0Case 1: b>0, implying in Statement 1 that a>c and in Statement 2 that a<0
Linking together c<a and a<0, we get:
c<a<0
Since a is between c and 0, the answer to the question stem is YES.
Case 2: b<0, implying in Statement 1 that a<c and in Statement 2 that a>0
Linking together 0<a and a<c, we get:
0<a<c
Since a is between c and 0, the answer to the question stem is YES.
In both cases, the answer to the question stem is YES.
SUFFICIENT.
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