Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 28 Feb 2012
Posts: 112
Concentration: Strategy, International Business
GPA: 3.9
WE: Marketing (Other)

If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
Updated on: 31 Aug 2012, 06:01
Question Stats:
76% (00:55) correct 24% (01:00) wrong based on 351 sessions
HideShow timer Statistics
If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true? A. c > b B. d > a C. b/c < d/a D. a/c > d/b E. (cd)2 < (ab)2 Could someone explain how to cross multiply such enequalities, what is the general rule?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If you found my post useful and/or interesting  you are welcome to give kudos!
Originally posted by ziko on 31 Aug 2012, 05:50.
Last edited by Bunuel on 31 Aug 2012, 06:01, edited 1 time in total.
Edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 46287

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
31 Aug 2012, 06:01
ziko wrote: If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?
A. c > b B. d > a C. b/c < d/a D. a/c > d/b E. (cd)2 < (ab)2
Could someone explain how to cross multiply such enequalities, what is the general rule? When you multiply/divide both parts of an inequality by a positive value you should keep the sign. When you multiply/divide both parts of an inequality by a negative value you should flip the sign. Now, if we multiply both parts of the given inequality by 1/(ac) (which according to the stem must be positive), then we'll get: b/c>d/a, so option C which says that b/c < d/a cannot be true. Answer: C.
_________________
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



Retired Moderator
Joined: 23 Oct 2011
Posts: 268

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
24 Sep 2012, 22:03
Hi All, Is there a way to verify the validity of options a and b. If answer c was also a valid inequality, how could we have verified the first two options? any inputs on this anyone? Thanks in advance.
_________________
******************** Push +1 kudos button please, if you like my post.



Intern
Joined: 11 Jul 2012
Posts: 41

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
31 Oct 2012, 15:12
ab > cd ab/abcd > cd/abcd 1/cd > 1/ab cd < ab ==> d/a < b/c (b/c CANNOT BE < d/a) Brother Karamazov



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11815
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
13 Feb 2015, 19:48
Hi All, This question can be solved by TESTing VALUES. Since there are so many variables, and the answers look a "little crazy", the key is to keep your numbers small and simple. We're told that (A)(B) > (C)(D) and that A, B, C and D are all POSITIVE. We're asked which of the following CANNOT be true. If we can prove that an answer COULD be true, even once, then we can eliminate it. Let's TEST VALUES: Starting with Answer A, is there a way for C to be > B? IF.... A = 3 B = 2 C = 3 D = 1 Here, C is greater than B. Eliminate Answer A. We can ALSO eliminate a couple of other answers with this example: Answer D (3/3 > 1/2) and Answer E (3^2 < 6^2) can be eliminated TOO. With 2 answers remaining, I'm going to deal with the easierlooking option: With Answer B, is there a way for D to be > A? IF... A = 3 B = 2 C = 1 D = 4 Here, D is greater than A. Eliminate Answer B. The final answer is the only one left.... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 26 Jun 2012
Posts: 6

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
14 Nov 2015, 19:28
if you take a=3 b=4 c=2 d=1 even option c will be true 3*4>2*1 and b/c>d/a 4/2>1/3 so even option C is true Can you correct me if i am wrong. Some thing wrong in this question



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11815
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
14 Nov 2015, 21:27
Hi ashokingmat, If you compare your work to Answer C in the original prompt, you'll notice that you've used the WRONG inequality. Answer C: B/C < D/A You wrote it as B/C > D/A. Your example is a good one though (it does prove that C is not true), you just made a little mistake in your work. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 09 Nov 2016
Posts: 56

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
31 Jul 2017, 05:04
Its C.. I was stuck between B & C only. B can be sometimes true, but C can never be true. Hence, C.



Director
Joined: 13 Mar 2017
Posts: 610
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
31 Jul 2017, 06:34
ziko wrote: If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?
A. c > b B. d > a C. b/c < d/a D. a/c > d/b E. (cd)2 < (ab)2
Could someone explain how to cross multiply such enequalities, what is the general rule? a,b,c,d > 0 ab>cd A. INCORRECT. Can/Cannot be TRUE: as c can be greater than b or less than b. We can't say which is greater B. INCORRECT . Can/Cannot be TRUE: Again similar to option A, here also d can be greater than or less than a. We can't say which is greater. C. CORRECT. Cannot be TRUE: ab>cd > b/c > d/a. So, b/c < d/a is totally incorrect. D. INCORRECT. a/c > d/b This is totally possible. E. INCORRECT. (ab)^2 > (cd)^2. This is also true. Answer C
_________________
CAT 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570

Re: If ab > cd and a, b, c and d are all greater than zero [#permalink]
Show Tags
01 Aug 2017, 17:05
ziko wrote: If ab > cd and a, b, c and d are all greater than zero, which of the following CANNOT be true?
A. c > b B. d > a C. b/c < d/a D. a/c > d/b E. (cd)2 < (ab)2 We can divide the given inequality by ac since we know that all of our variables are greater than zero: ab/(ac) > cd/(ac) b/c > d/a Since b/c will always be greater than d/a, b/c < d/a can NEVER be true. Answer: C
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: If ab > cd and a, b, c and d are all greater than zero
[#permalink]
01 Aug 2017, 17:05






