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# Is ab < 0?

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Senior Manager
Joined: 02 Jan 2017
Posts: 315

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13 Mar 2017, 03:48
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Difficulty:

25% (medium)

Question Stats:

76% (01:03) correct 24% (00:47) wrong based on 29 sessions

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Is ab < 0?

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

(2) $$a(bc)^6 > 0$$
[Reveal] Spoiler: OA
Manager
Joined: 16 Oct 2015
Posts: 73
Location: India
Concentration: Technology, General Management
GMAT 1: 520 Q44 V17
GMAT 2: 530 Q44 V20
GMAT 3: 710 Q48 V40
GPA: 3.45
WE: Research (Energy and Utilities)
Re: Is ab < 0? [#permalink]

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13 Mar 2017, 04:05
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

Sent from my MI 3W using GMAT Club Forum mobile app
Manager
Joined: 08 Oct 2015
Posts: 95
Re: Is ab < 0? [#permalink]

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13 Mar 2017, 04:26
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

Sent from my MI 3W using GMAT Club Forum mobile app

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

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

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13 Mar 2017, 05:37
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.

_________________
Manager
Joined: 16 Oct 2015
Posts: 73
Location: India
Concentration: Technology, General Management
GMAT 1: 520 Q44 V17
GMAT 2: 530 Q44 V20
GMAT 3: 710 Q48 V40
GPA: 3.45
WE: Research (Energy and Utilities)
Re: Is ab < 0? [#permalink]

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13 Mar 2017, 06:27
rahulkashyap wrote:
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

Sent from my MI 3W using GMAT Club Forum mobile app

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.

Sent from my MI 3W using GMAT Club Forum mobile app
Re: Is ab < 0?   [#permalink] 13 Mar 2017, 06:27
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