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Is ab < 0?

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Is ab < 0? [#permalink]

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New post 13 Mar 2017, 04:48
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A
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C
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E

Difficulty:

  25% (medium)

Question Stats:

74% (01:05) correct 26% (00:46) wrong based on 31 sessions

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Is ab < 0?

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

(2) \(a(bc)^6 > 0\)
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Re: Is ab < 0? [#permalink]

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New post 13 Mar 2017, 05:05
Answer is C.
From first statement we can surely conclude that "b" is negative. However "a" can be positive or negative.

second statement implies "a" is positive. But gives no clue about "b"

Combining both statements we can conclude ab<0



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Re: Is ab < 0? [#permalink]

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New post 13 Mar 2017, 05:26
askul2389 wrote:
Answer is C.
From first statement we can surely conclude that "b" is negative. However "a" can be positive or negative.

second statement implies "a" is positive. But gives no clue about "b"

Combining both statements we can conclude ab<0



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Can you pls explain how you solved statement 1 to get your answer?

chetan2u pls help
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Re: Is ab < 0? [#permalink]

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New post 13 Mar 2017, 06:37
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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Re: Is ab < 0? [#permalink]

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New post 13 Mar 2017, 07:27
rahulkashyap wrote:
askul2389 wrote:
Answer is C.
From first statement we can surely conclude that "b" is negative. However "a" can be positive or negative.

second statement implies "a" is positive. But gives no clue about "b"

Combining both statements we can conclude ab<0



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Can you pls explain how you solved statement 1 to get your answer?

chetan2u pls help

a^4b^9c^2<0

Here, since a and c have even exponents, a4 and c2 will always be positive.

Since, a4*b9*c2 is less than zero (negative value) , b will have to be negative.

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Re: Is ab < 0?   [#permalink] 13 Mar 2017, 07:27
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