If ab^3c^4 > 0, is a^3bc^5 > 0? : Data Sufficiency (DS)

2015-06-12T03:38:05-07:00

If [m]ab^3c^4 > 0[/m], is [m]a^3bc^5 > 0[/m]? (1) b > 0 (2) c > 0 [b]Kudos for a correct [i]solution[/i].[/b]

ShristiK

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

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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Bunuel

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

15 Jun 2015, 05:57

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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.

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]

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]

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]

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]

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]

22 Apr 2018, 21:49

Expert Reply

selim wrote:

If \(ab^3c^4>0 is a^3bc^5>0?\)

1.b>0
2.c>0

___________________________
Merging topics.

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

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

Posted from my mobile device

B

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

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"

B

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

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)

B

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

21 Feb 2019, 03:48

Bunuel wrote:

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

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

Kudos for a correct solution.

\(ab^3c^4 > 0\)
gives,
\(ab^3 > 0\) i.e., we have\(ab>0\)

i. a>0 b>0
ii. a<0 b<0

to find if
\(a^3bc^5 > 0\)
we already know that \(ab > 0\)
which implies \(a^3b > 0\)
so if c>0 the \(a^3bc^5 > 0\) is true
else false

(1) given b>0 ---> insufficient
(2) given c>0 ----> sufficient

option is B
----------------------------------------
Please leave a kudos:)

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

16 Mar 2021, 08:27

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Bunuel wrote:

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

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

As \(ab^3c^4 > 0\) so either a & b both are positive or both are negative.

(1) we don't know about a and c. \(a^3bc^5\) could be \(a^3bc^5 > 0\) or \(a^3bc^5 < 0\) with respect to the value of a and c.

(2) As c > 0 and \(ab^3c^4 > 0\) so a must positive. Then \(a^3bc^5 > 0\). Sufficient.

The answer is B.