Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50001

If ab^3c^4 > 0, is a^3bc^5 > 0?
[#permalink]
Show Tags
12 Jun 2015, 03:38
Question Stats:
64% (00:56) correct 36% (01:07) wrong based on 296 sessions
HideShow timer Statistics



CEO
Joined: 08 Jul 2010
Posts: 2549
Location: India
GMAT: INSIGHT
WE: Education (Education)

If ab^3c^4 > 0, is a^3bc^5 > 0?
[#permalink]
Show Tags
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
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
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.



Manager
Joined: 26 Dec 2011
Posts: 114

Re: If ab^3c^4 > 0, is a^3bc^5 > 0?
[#permalink]
Show Tags
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
_________________
Thanks, Kudos Please



Intern
Joined: 26 Aug 2014
Posts: 46
GMAT 1: 650 Q49 V30 GMAT 2: 650 Q49 V31
WE: Programming (Computer Software)

Re: If ab^3c^4 > 0, is a^3bc^5 > 0?
[#permalink]
Show Tags
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
Press Kudos if you like it!



Math Expert
Joined: 02 Sep 2009
Posts: 50001

Re: If ab^3c^4 > 0, is a^3bc^5 > 0?
[#permalink]
Show Tags
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 24 Oct 2013
Posts: 142
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)

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



Director
Joined: 26 Oct 2016
Posts: 642
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If ab^3c^4 > 0, is a^3bc^5 > 0?
[#permalink]
Show Tags
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.
_________________
Thanks & Regards, Anaira Mitch



Director
Joined: 31 Oct 2013
Posts: 650
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)

If ab^3c^4>0 is a^3bc^5>0 ?
[#permalink]
Show Tags
22 Apr 2018, 07:03
If \(ab^3c^4>0 is a^3bc^5>0?\)
1.b>0 2.c>0



Manager
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)

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



Math Expert
Joined: 02 Sep 2009
Posts: 50001

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



Director
Joined: 02 Oct 2017
Posts: 649

Re: If ab^3c^4 > 0, is a^3bc^5 > 0?
[#permalink]
Show Tags
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
_________________
Give kudos if you like the post



Intern
Joined: 14 Mar 2015
Posts: 5
Location: India
GPA: 3.57

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



Intern
Joined: 19 Sep 2014
Posts: 2
WE: Engineering (Manufacturing)

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




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






