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

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Bunuel
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Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0 [#permalink] New post   18 Nov 2019, 02:00
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79% (01:02) correct 21% (01:17) wrong based on 125 sessions
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Is \(ab < 0\)?

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

(2) \(a(bc)^6 > 0\)
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C
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lacktutor
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Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0 [#permalink] New post   18 Nov 2019, 02:10
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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

The answer is C

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Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0 [#permalink] New post   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

The answer is C

Posted from my mobile device




Can you please explain why b <0 in (1) and a > 0 in (2) :cry:
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Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0 [#permalink] New post   25 Nov 2019, 11:13
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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

The answer is C

Posted from my mobile device




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


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
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merajul
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Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0 [#permalink] New post   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

The answer is C

Posted from my mobile device




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


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
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Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0 [#permalink] New post   24 Oct 2023, 06:15
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Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0 [#permalink]
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