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If ab^3c^4 > 0, is a^3bc^5 > 0?
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12 Jun 2015, 03:38
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If \(ab^3c^4 > 0\), is \(a^3bc^5 > 0\)? (1) b > 0 (2) c > 0 Kudos for a correct solution.
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If ab^3c^4 > 0, is a^3bc^5 > 0?
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Updated on: 11 Sep 2018, 08:24
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 signQuestion : is \(a^3bc^5 > 0\)But \(a^3b\) will always be positive as a and b have same signi.e. We only need to find the sign of c to answer the questionStatement 1: b > 0Sign of c is unknown Hence, NOT SUFFICIENTStatement 2: c > 0i.e. c is positive therefore \(a^3bc^5 > 0\) is True Hence, SUFFICIENTAnswer: 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?
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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 Thanks Please give me Kudos
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?
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13 Jun 2015, 02:50
(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?
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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?
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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?
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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 ?
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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 ?
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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?
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22 Apr 2018, 21:49
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?
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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
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Re: If ab^3c^4 > 0, is a^3bc^5 > 0?
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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?
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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?
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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:)




Re: If ab^3c^4 > 0, is a^3bc^5 > 0?
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21 Feb 2019, 03:48






