Bunuel wrote:
Is ab < 0?
(1) \(a^4b^9c^2 < 0\)
(2) \(a(bc)^6 > 0\)
It should be C.
Statement 1: Since a and c have even powers, expression is less than 0 only because b is negative. However, we do not know the sign of a as a^4 would be +ive in all cases.
Statement 2: we can know a is positive since \((bc)^6\) can only be positive. However, we do not know if b is positive.
Combined.
From 1, we know b is negative and from 2 we know a is positive, so combined the two expressions are sufficient to answer the question. An important aspect to note is both expressions result in values greater or less than 0 which suggests none of these numbers is zero.
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