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

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

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New post 12 Jul 2017, 01:06
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (00:55) correct 21% (01:14) wrong based on 61 sessions

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

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New post 12 Jul 2017, 01:59
4
Bunuel wrote:
Is ab < 0?

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

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


It should be C.

Statement 1: Since a and c have even powers, expression is less than 0 only because b is negative. However, we do not know the sign of a as a^4 would be +ive in all cases.
Statement 2: we can know a is positive since \((bc)^6\) can only be positive. However, we do not know if b is positive.

Combined.
From 1, we know b is negative and from 2 we know a is positive, so combined the two expressions are sufficient to answer the question. An important aspect to note is both expressions result in values greater or less than 0 which suggests none of these numbers is zero.
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Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0  [#permalink]

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New post 12 Jul 2017, 07:35
Should be C :
From first option we can conclude that just b is negative , no information about A
From second option we can conclude that a definitely must be positive
Combining statement A & B , we can conclude that ab <0 - Sufficient
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Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0  [#permalink]

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New post 12 Jul 2017, 19:11
A.

statement 1:for equation to be less than zero, b has to be -ve (as a and c are even power thus does not effect the equ.)
thus stat 1 alone sufficient.
stat 2:a has to be +ve for the equ to be true. b and c can be +ve or -ve (since even power; we can't say much).thus stat 2 insuff.

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

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New post 12 Jul 2017, 19:30
For ab<O ie be negative either a or b has to be negative. If both are negative than ab will be >0
In short we need to know the sign of a and b.
statement 1. The expression is less than 0. Any negative no raised to an even power will be +ve. In the expression only b is raised to an odd power and is negative. we are not sure about a. Insufficient
Statement 2. The expression is +ve only possible if a is positive Since other part of the expression is raised to an even power. This statement does not give any information on B. Insufficient.
combine both the statements. b is negative and a is positive. hence above is negative or <0. Answer C.

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

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New post 12 Jul 2017, 19:31
For ab<O ie be negative either a or b has to be negative. If both are negative than ab will be >0
In short we need to know the sign of a and b.
statement 1. The expression is less than 0. Any negative no raised to an even power will be +ve. In the expression only b is raised to an odd power and is negative. we are not sure about a. Insufficient
Statement 2. The expression is +ve only possible if a is positive Since other part of the expression is raised to an even power. This statement does not give any information on B. Insufficient.
combine both the statements. b is negative and a is positive. hence above is negative or <0. Answer C.

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

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Re: Is ab < 0? (1) a^4b^9c^2 < 0 (2) a(bc)^6 > 0   [#permalink] 02 Apr 2019, 19:41
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