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If a^5b^3c^6 < 0, is abc < 0?

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fozzzy
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If a^5b^3c^6 < 0, is abc < 0? [#permalink] New post   Updated on: 08 Jul 2013, 00:43
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56% (01:17) correct 44% (01:18) wrong based on 198 sessions
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If \(a^5b^3c^6 < 0\), is abc < 0?

(1) b < 0
(2) c > 0

Any alternative solutions?
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B

Originally posted by fozzzy on 08 Jul 2013, 00:40.
Last edited by Bunuel on 08 Jul 2013, 00:43, edited 1 time in total.
Edited the question.
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Re: If a^5b^3c^6 < 0, is abc < 0? [#permalink] New post   08 Jul 2013, 00:47
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If \(a^5b^3c^6 < 0\), is abc < 0?

\(a^5b^3c^6 < 0\) --> reduce by \(a^4b^2c^6\) (notice that this expression is positive): \(ab< 0\). Since, \(ab< 0\), then \(abc < 0\), when \(c>0\).

(1) b < 0. Not sufficient.
(2) c > 0. Sufficient.

Answer: B.

Hope it's clear.
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Re: If a^5b^3c^6 < 0, is abc < 0? [#permalink] New post   07 Apr 2015, 14:34
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Hi All,

This question is packed full of Number Properties, which you can use to answer the question.

We're told that (A^5)(B^3)(C^6) < 0. This tells us a few things:

1) NONE of the variables can equal 0 (since the product is LESS than 0)
2) C could be positive or negative.
3) Between A and B, one is positive while the other is negative.

The question asks if (A)(B)(C) is < 0. This is a YES/NO question.

Since we know that A and B will give us one positive and one negative, (A)(B) MUST be negative. Thus, the question 'hinges' on C....
IF....C = postive, then the product of (A)(B)(C) is negative and the answer to the question is YES.
IF....C = negative, then the product of (A)(B)(C) is positive and the answer to the question is NO.

Fact 1: B < 0

This tells us that A MUST be positive, but it tells us nothing about C.
Fact 1 is INSUFFICIENT

Fact 2: C > 0

This provides the essential piece of information that we need. We now know that the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer:
Show Spoiler
B


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Re: If a^5b^3c^6 < 0, is abc < 0? [#permalink] New post   08 Jul 2013, 01:57
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fozzzy wrote:
If \(a^5b^3c^6 < 0\), is abc < 0?

(1) b < 0
(2) c > 0

Any alternative solutions?


You can also do it so,

\(a^5b^3c^6 < 0\) = \((abc)^3 * a^2c^3 < 0\)

(1) b< 0 this doesn't tell us anything about the left hand side of the inequality

Insufficent

(2) c > 0 , now this means that the second term in the modified left hand side .. \(a^2c^3 >0\). Thus the other term \(abc^3 < 0\). This implies that
\(abc < 0\)

Sufficient

Thus the answer is B
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Re: If a^5b^3c^6 < 0, is abc < 0? [#permalink] New post   07 Dec 2016, 09:27
fozzzy wrote:
If \(a^5b^3c^6 < 0\), is abc < 0?

(1) b < 0
(2) c > 0

Any alternative solutions?


from stem
a and b has different signs and thus if c is +ve is the deciding factor whether abc<0

from 1

irrelevant

from 2

c is +Ve thus abc<0 ... suff

b
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Re: If a^5b^3c^6 < 0, is abc < 0? [#permalink]
07 Dec 2016, 09:27
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Bunuel
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