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If ab^3c^4 > 0, is a^3bc^5 > 0?

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If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 12 Jun 2015, 03:38
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If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post Updated on: 11 Sep 2018, 08:24
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Bunuel wrote:
If \(ab^3c^4 > 0\), is \(a^3bc^5 > 0\)?

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

Kudos for a correct solution.


Given: \(ab^3c^4 > 0\)

i.e. a*b must be Positive [Odd powers don't change the sign of variable]
i.e. a and b have same sign


Question : is \(a^3bc^5 > 0\)

But \(a^3b\) will always be positive as a and b have same sign

i.e. We only need to find the sign of c to answer the question

Statement 1: b > 0

Sign of c is unknown

Hence, NOT SUFFICIENT

Statement 2: c > 0

i.e. c is positive therefore \(a^3bc^5 > 0\) is True

Hence, SUFFICIENT

Answer: option
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Originally posted by GMATinsight on 12 Jun 2015, 04:25.
Last edited by GMATinsight on 11 Sep 2018, 08:24, edited 5 times in total.
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 12 Jun 2015, 06:09
If ab^3c^4>0, is a^3bc^5>0?

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

Explanation -

Stmt 1 - If b is +ve, a is +ve and we do not know about c +ve or -ve. Not Sufficient

Stmt 2 - If c is +ve, both a and b must be +ve or -ve to meet the condition. Sufficient

Ans B
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 13 Jun 2015, 02:50
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(i) ab^3c^4>0
(ii) a^3bc^5>0?

Here, powers of a and b are odd in both inequalities so, their sign won't change to negative.
(Notice c^4 will always be positive so multiplication of odd powers of a with odd powers of b will also be always positive to satisfy (i)).

However, the power of c changes in both inequalities from even in (i) to odd in (ii).
Hence, if c is positive (ii) will be positive, and if c is negative (ii) will be negative.

(1) b > 0
This gives us no information on the sign of c, and consequently, we cannot determine if (ii) is positive or negative. Not Sufficient

(2) c > 0
This tells us c is positive. Hence (ii) is positive. Sufficient


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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 15 Jun 2015, 05:57
Bunuel wrote:
If \(ab^3c^4 > 0\), is \(a^3bc^5 > 0\)?

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

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Odd exponents do not “hide the sign” of the base. In other words, a and a^3 have the same sign, as do b and b^3, regardless of the signs of a and b. In comparing ab^3c^4 > 0 (the constraint) to a^3bc^5 (the question), the only unknown real difference is between c^4 and c^5. We know that c^4 must be positive (even exponent), so if we want c^5 to be positive, then c needs to be positive also. Our rephrased question is thus “Is c > 0?”

(1) INSUFFICIENT: No information about the sign of c.

(2) SUFFICIENT: Answers the rephrased question directly.

The correct answer is B.
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 27 Sep 2016, 06:24
a and b are odd powers in both the expressions. only unknown sign is of c

Statement 2 states C >0 => final value is positive.

HEnce B
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 03 Mar 2017, 13:16
Odd exponents do not “hide the sign” of the base. In other words, a and a^3 have the same sign, as do b and b^3, regardless of the signs of a and b. In comparing ab^3c^4 > 0 (the constraint) to a^3bc^5 (the question), the only unknown real difference is between c^4 and c^5. We know that c^4 must be positive (even exponent), so if we want c^5 to be positive, then c needs to be positive also. Our rephrased question is thus “Is c > 0?”
(1) INSUFFICIENT: No information about the sign of c.
(2) SUFFICIENT: Answers the rephrased question directly.
The correct answer is B.
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If ab^3c^4>0 is a^3bc^5>0 ?  [#permalink]

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New post 22 Apr 2018, 07:03
If \(ab^3c^4>0 is a^3bc^5>0?\)

1.b>0
2.c>0
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Re: If ab^3c^4>0 is a^3bc^5>0 ?  [#permalink]

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New post 22 Apr 2018, 07:17
selim wrote:
If \(ab^3c^4>0 is a^3bc^5>0?\)

1.b>0
2.c>0


from given statement either a>0,b>0 or a<0,b<0

From 1: we cant say anything.

From 2: since a and b have same sign Then a*b>0 . and c>0

Therefore \(a^3bc^5>0\)

Sufficient B.
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 22 Apr 2018, 21:49
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 08 May 2018, 09:52
ab^3c^4>0
Simply means a and b have same sign

So for a^3bc^5>0

Since a and b have same sign so only thing we need to know whether c>0 or not

Choice B states this

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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 11 Sep 2018, 10:17
Bunuel wrote:
If \(ab^3c^4 > 0\), is \(a^3bc^5 > 0\)?

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

Kudos for a correct solution.


Hi,

Given ab^3c^4 > 0. We already know that any integer multiplied to even power is always positive.

Hence from above we already now that b^2 and c^4 are always positive. Hence this inequation input can be simplified to ab>0. This is the given input.

Now the question " is a^3bc^5 > 0"?

Again applying above discussed funda, the question can be simplified to is abc>0?

So the question is if ab>0, is abc >o?

From options, it is clear that "option 1 : b >0 " is not sufficient whereas "option 2 : c>0" alone is sufficient to answer.

Hence option "B"
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?  [#permalink]

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New post 27 Sep 2018, 06:15
If ab^3c^4 > 0, is a^3bc^5 > 0?

Now coming to first equation: as c^4 term is present, being exponent an even power it has no effect on overall equation.
Hence coming on ab, as ab>0 then definitely a & b are of same sign either both + or both -.

Hence deciding factor is c for the next equation as it has odd exponent, only if its is> 0 then only the whole equation is > 0.

So Statement 2 is true.

Ans. (B)
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0? &nbs [#permalink] 27 Sep 2018, 06:15
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