|x-z| = the distance between x and z.
|x| = the distance between x and 0.
|z| = the distance between z and 0.
Constraint in the question stem: zy < xy < 0.
Case 1: If y is POSITIVE, then x and z are NEGATIVE, with z "more negative" than x, so that zy < xy.
Case 2: If y is NEGATIVE, then x and z are POSITIVE, with z "more positive" than x, so that zy < xy.
Case 1:
z<---|x-z|--->x<---|x|--->0..........y
In the number line above, the red portion represents |z|: the distance between z and 0.
|x-z| + |x| is equal to the red portion.
Thus:
|x-z| + |x| = |z|.
Case 2:
y..........0<---|x|--->x<---|x-z|--->z
In the number line above, the red portion represents |z|: the distance between z and 0.
|x-z| + |x| is equal to the red portion.
Thus:
|x-z| + |x| = |z|.
The two statements are IRRELEVANT.
Given that zy < xy < 0, it will ALWAYS be true that |x-z| + |x| = |z|.
Thus:
in statement 1, the answer to the question stem is YES, since it will always be true that |x-z| + |x| = |z|.
In statement 2, the answer to the question stem is YES, since it will always be true that |x-z| + |x| = |z|.
The correct answer is
D.
Since the two statements are irrelevant, this problem is flawed.
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