Question stem, rephrased:rsarashi wrote:Is a/b <0
A) a^2/b^3>0
B) ab^4<0
Do a and b have DIFFERENT SIGNS?
Statement 1: a²/b³ > 0
This inequality is valid only if a and b are both NONZERO.
Since the square of a nonzero value must be POSITIVE, b²/a² > 0.
Since b²/a² > 0, both sides of the inequality can safely be multiplied both by b²/a²:
(a²/b³)(b²/a²) > 0(b²/a²)
1/b > 0.
The inequality in blue implies that b>0.
No information about a.
INSUFFICIENT.
Statement 2: ab� < 0
This inequality is valid only if a and b are both NONZERO.
Since a nonzero value raised to an even exponent must be POSITIVE, b� > 0.
Since b� > 0, both sides of the inequality can safely be divided both by b�:
(ab�)/b� < 0/b�
a < 0.
No information about b.
INSUFFICIENT.
Statements combined:
Statement 1 implies that b>0.
Statement 2 implies that a<0.
Thus, a and b have different signs.
SUFFICIENT.
The correct answer is C.
