LUANDATO wrote:$$If\ \ a^5b^6c^7>0,\ is\ ab>0?$$
$$1.b<0$$
$$2.c>0$$
a�b�c� > 0 implies that a, b and c are all NONZERO.
A nonzero value raised to an even power is positive.
Thus, we safely divide the inequality above by any even power of a, b and c.
If we divide each side by a�b�c�, we get:
a�b�c�/a�b�c� > 0/a�b�c�
ac > 0.
The resulting inequality indicate that a and c have the SAME SIGN.
The inequality in the question stem -- ab > 0 -- is valid only if a and b have the same sign.
Thus, the answer to the question stem will be YES only if a, b and c all have the same sign.
Question stem, rephrased:
If a and c have the same sign, do a, b and c all have the same sign?
Statement 1:
No information about the sign of a and c.
INSUFFICIENT.
Statement 2:
Since c is negative -- and a and c have the sign sign -- a is negative.
No information about the sign of b.
INSUFFICIENT.
Statements combined:
Statement 1 indicates that b is positive.
Statement 2 indicates that a and c are negative.
Thus:
a, b and c do NOT all have the same sign, with the result that the answer to the question stem is NO.
SUFFICIENT.
The correct answer is
C.
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