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# Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0

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Math Expert
Joined: 02 Sep 2009
Posts: 59622
Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0  [#permalink]

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18 Nov 2019, 02:00
00:00

Difficulty:

35% (medium)

Question Stats:

72% (00:53) correct 28% (01:20) wrong based on 36 sessions

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Is $$ab < 0$$?

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

(2) $$a(bc)^6 > 0$$

_________________
Senior Manager
Joined: 25 Jul 2018
Posts: 395
Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0  [#permalink]

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18 Nov 2019, 02:10
Is ab <0?

(Statement1):
$$a^{4}*b^{9}*c^{2} <0$$
—> we can simplify —> b <0

a can be positive or negative
Insufficient

Statement2): $$a(bc)^{6} > 0$$
—> we can simplify —> a > 0

b can be positive or negative
Insufficient

Taken together 1&2,
a > 0 and b <0
—> ab is always less than zero
(ab <0)

Sufficient

Posted from my mobile device
Manager
Joined: 05 Oct 2014
Posts: 122
Location: India
Concentration: General Management, Strategy
GMAT 1: 580 Q41 V28
GPA: 3.8
WE: Project Management (Energy and Utilities)
Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0  [#permalink]

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25 Nov 2019, 10:41
lacktutor wrote:
Is ab <0?

(Statement1):
$$a^{4}*b^{9}*c^{2} <0$$
—> we can simplify —> b <0

a can be positive or negative
Insufficient

Statement2): $$a(bc)^{6} > 0$$
—> we can simplify —> a > 0

b can be positive or negative
Insufficient

Taken together 1&2,
a > 0 and b <0
—> ab is always less than zero
(ab <0)

Sufficient

Posted from my mobile device

Can you please explain why b <0 in (1) and a > 0 in (2)
Senior Manager
Joined: 25 Jul 2018
Posts: 395
Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0  [#permalink]

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25 Nov 2019, 11:13
1
merajul wrote:
lacktutor wrote:
Is ab <0?

(Statement1):
$$a^{4}*b^{9}*c^{2} <0$$
—> we can simplify —> b <0

a can be positive or negative
Insufficient

Statement2): $$a(bc)^{6} > 0$$
—> we can simplify —> a > 0

b can be positive or negative
Insufficient

Taken together 1&2,
a > 0 and b <0
—> ab is always less than zero
(ab <0)

Sufficient

Posted from my mobile device

Can you please explain why b <0 in (1) and a > 0 in (2)

Hi,
—> Dividing (or Multiplying)the both sides by the same positive number does not change the sign of an inequality.
—> (Statement1): The exponents of ‘a’ and ‘c’ are even —>$$a^{4}$$ and $$c^{2}$$ are positive numbers.
—> you can divide both sides by both positive numbers, it does not change the sign and you’ll get b< 0.

The same as statement2
Hope it helps
Manager
Joined: 05 Oct 2014
Posts: 122
Location: India
Concentration: General Management, Strategy
GMAT 1: 580 Q41 V28
GPA: 3.8
WE: Project Management (Energy and Utilities)
Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0  [#permalink]

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25 Nov 2019, 11:18
lacktutor wrote:
merajul wrote:
lacktutor wrote:
Is ab <0?

(Statement1):
$$a^{4}*b^{9}*c^{2} <0$$
—> we can simplify —> b <0

a can be positive or negative
Insufficient

Statement2): $$a(bc)^{6} > 0$$
—> we can simplify —> a > 0

b can be positive or negative
Insufficient

Taken together 1&2,
a > 0 and b <0
—> ab is always less than zero
(ab <0)

Sufficient

Posted from my mobile device

Can you please explain why b <0 in (1) and a > 0 in (2)

Hi,
—> Dividing (or Multiplying)the both sides by the same positive number does not change the sign of an inequality.
—> (Statement1): The exponents of ‘a’ and ‘c’ are even —>$$a^{4}$$ and $$c^{2}$$ are positive numbers.
—> you can divide both sides by both positive numbers, it does not change the sign and you’ll get b< 0.

The same as statement2
Hope it helps

Ah!!! now able to understand. Thank You
Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0   [#permalink] 25 Nov 2019, 11:18
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