vikasp99 wrote:

Is ab < 0?

(1) a^4b^9c^2 < 0

(2) a(bc)^6 > 0

(1) \(a^4b^9c^2 < 0 \implies b^9 < 0\) since \(a^4 \geq 0\) and \(c^2 \geq 0\) \(\forall a,c \in R\).

Hence, \(b < 0\).

If \(a>0 \implies ab < 0\)

If \(a<0 \implies ab > 0\).

Hence, insufficient.

(2) \(a \times (bc)^6 > 0 \implies a > 0\) since \((bc)^6 \geq 0 \; \forall b,c \in R\).

If \(b>0 \implies ab > 0\)

If \(b<0 \implies ab < 0\).

Hence, insufficient.

Combine (1) & (2)

From (1) we have \(b<0\)

From (2) we have \(a>0\)

Hence \(ab<0\), sufficient.

The answer is C.

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