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a and b could be fractions. We are not assuming that they must be integers. We are only talking about their sign.
(1)a^2/b^3 > 0
It doesn't matter whether a and b are fractions or integers, a^2 will be positive. So b must be positive since positive/b^3 is positive. But we don't know whether a is positive or negative. Can't say about the sign of a/b
(2) ab^4 < 0
b^4 must be positive. So a must be negative because a/positive is negative. Can't say about the sign of a/b
Both together, b is positive and a is negative so a/b must be negative. Sufficient.
Prompt analysis A and b are real numbers. Superset The answer will be either YES or NO.
Translation In order to find the answer, we need: 1# exact value of a and b. 2# any equation to find the a and b 3# any equation to find the exact or the range for a/b
Statement analysis St 1: a^2/b^3 >0. a^2 is always greater than zero. If the complete expression is positive, that means that b^3 is positive hence b is positive. But nothing can be said about a. INSUFFICIENT
St 2: ab^4<0. b^4 is always positive.nothing can be said about b though. To make the expression negative, a has to be negative.
St 1 & St 2: from st 1, we can say that b>0. From st 2, we can say that a<0. Therefore a/b <0. Option C.