Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 18 Aug 2009
Posts: 284

If ab ≠ 0, does a=b?
[#permalink]
Show Tags
Updated on: 11 Oct 2013, 03:27
Question Stats:
58% (01:35) correct 42% (01:16) wrong based on 332 sessions
HideShow timer Statistics
If ab ≠ 0, does a=b? (1) x^a = x^b (2) xa = xb
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by gmattokyo on 06 Nov 2009, 08:36.
Last edited by Bunuel on 11 Oct 2013, 03:27, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



Manager
Status: done, waiting fingerss crossed!
Joined: 01 Jul 2009
Posts: 117
Location: India
Concentration: Entrepreneurship, Strategy
GPA: 3.8
WE: General Management (Retail)

Re: is a=b
[#permalink]
Show Tags
06 Nov 2009, 09:23
whats " <> " ??
_________________
i love kudos consider giving them if you like my post!!
CRITICAL REASONING FOR BEGINNERS: notes & links to help you learn CR better. Click Below http://gmatclub.com/forum/criticalreasoningforbeginners82111.html QUANT NOTES FOR PS & DS: notes to help you do better in Quant. Click Below http://gmatclub.com/forum/quantnotesforpsds82447.html GMAT Timing Planner: This little tool could help you plan timing strategy. Click Below http://gmatclub.com/forum/gmatcattimingplanner82513.html



Manager
Joined: 04 Nov 2009
Posts: 64
Schools: London Business School (int)
WE 1: Research
WE 2: Corporate Strat

Re: is a=b
[#permalink]
Show Tags
06 Nov 2009, 09:51
E  Neither is sufficient.
Whether we take each statement or them together, the options are either a=b or x=0. Can't answer for sure.



Director
Joined: 01 Apr 2008
Posts: 792
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: is a=b
[#permalink]
Show Tags
06 Nov 2009, 11:08
guess gmattokyo is a programmer:), coz "<>" stands for 'not equal to' in some programming language I guess.
I go with C. stmt1: x can be 1, a and b can be same or different.
stmt2: a = b => magnitude of a and b is same, signs can be different.
Combining, a and b should have the same sign, it is not possible to have one value positive and the other negative. So they should be same.
For x=0, a and b can only be positive, as 1/0 is not defined.



Manager
Joined: 04 Nov 2009
Posts: 64
Schools: London Business School (int)
WE 1: Research
WE 2: Corporate Strat

Re: is a=b
[#permalink]
Show Tags
06 Nov 2009, 11:37
Great catch  missed that if x=0, a and b would have to be positive.
But even if we take the two statements together, couldn't
1. x=0, (a,b) = (2,3) This would satisfy x^a = x^b as well as xa=xb or 2. x=1, (a,b) = (4,4) This would satisfy x^a = x^b as well as xa=xb
So shouldn't it be E?



Director
Joined: 01 Apr 2008
Posts: 792
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: is a=b
[#permalink]
Show Tags
06 Nov 2009, 11:42
You are right I missed it. in stmt2: we cannot cancel out x until we know that x is not equal to zero. E should be the answer.



Manager
Joined: 08 Jul 2009
Posts: 153

Re: is a=b
[#permalink]
Show Tags
06 Nov 2009, 15:03
Think about this way if x = 1 or 0
then if a = 1 and b= 1
both statements are satisfied but a not = b



Senior Manager
Joined: 18 Aug 2009
Posts: 284

Re: is a=b
[#permalink]
Show Tags
06 Nov 2009, 19:27
sher676 wrote: Think about this way if x = 1 or 0
then if a = 1 and b= 1
both statements are satisfied but a not = b Thats correct. OA: Key here is to think about x also and run it through the zero, integer, negative test. And as sher676 said, for x=1 and x=0 there maybe many combination of a & b! Economist, you got that right.. I actually was looking for a while how to put a "crossed=" We can use neq with the math button \(ab \neq 0\)



Manager
Joined: 16 Jul 2009
Posts: 207

Re: is a=b
[#permalink]
Show Tags
07 Nov 2009, 11:45
Thats a gud 1 gmattokyo, (zero, integer and negative test)  if this test is used many DS ques can be answered correctly. Thanks for tht tip! Going by this the [E] has to be the answer..



Manager
Joined: 29 Oct 2009
Posts: 197

Re: is a=b
[#permalink]
Show Tags
07 Nov 2009, 11:53
good question.. not difficult but a little tricky! thanks for your constant supply of questions gmattokyo.. providing some good practice!
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Senior Manager
Joined: 18 Aug 2009
Posts: 284

Re: is a=b
[#permalink]
Show Tags
07 Nov 2009, 20:10
sriharimurthy wrote: good question.. not difficult but a little tricky! thanks for your constant supply of questions gmattokyo.. providing some good practice! Thanks sriharimurthy. glad ur finding it of help lets crack GMAT (and try remain sane at the same time)!



Manager
Joined: 29 Oct 2009
Posts: 197

Re: is a=b
[#permalink]
Show Tags
08 Nov 2009, 10:04
gmattokyo wrote: sriharimurthy wrote: good question.. not difficult but a little tricky! thanks for your constant supply of questions gmattokyo.. providing some good practice! Thanks sriharimurthy. glad ur finding it of help lets crack GMAT (and try remain sane at the same time)! Haha. Cheers to that gmattokyo!
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



SVP
Joined: 06 Sep 2013
Posts: 1764
Concentration: Finance

Re: if ab <> 0, is a=b? 1) x^a = x^b 2) xa=xb
[#permalink]
Show Tags
10 Oct 2013, 15:47
gmattokyo wrote: if ab <> 0, is a=b?
1) \(x^a = x^b\) 2) \(xa=xb\) I'm a bit suprised to find that the answer is (E) Statement 1 is clearly insuff Statement 2 though xa=xb, so a/b = 1. Hence since the answer is positive, both need to be negative or both need to be positive. In any case a = b. I wonder what am I doing wrong here. Experts please advice Thank you Cheers



Manager
Joined: 29 Aug 2013
Posts: 74
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q41 V29 GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)

Re: if ab <> 0, is a=b? 1) x^a = x^b 2) xa=xb
[#permalink]
Show Tags
11 Oct 2013, 03:18
jlgdr wrote: gmattokyo wrote: if ab <> 0, is a=b?
1) \(x^a = x^b\) 2) \(xa=xb\) I'm a bit suprised to find that the answer is (E) Statement 1 is clearly insuff Statement 2 though xa=xb, so a/b = 1. Hence since the answer is positive, both need to be negative or both need to be positive. In any case a = b. I wonder what am I doing wrong here. Experts please advice Thank you Cheers Hi, a and b has to be positive; they can not be negative since they are absolute values. Moreover when we have a = b; a and b can be positive/negative for eg. a=2 b=2 ; Therefore a = b = 2. Consider Kudos if the post helps!!!



Math Expert
Joined: 02 Sep 2009
Posts: 49970

Re: if ab <> 0, is a=b? 1) x^a = x^b 2) xa=xb
[#permalink]
Show Tags
11 Oct 2013, 05:05
jlgdr wrote: gmattokyo wrote: if ab <> 0, is a=b?
1) \(x^a = x^b\) 2) \(xa=xb\) I'm a bit suprised to find that the answer is (E) Statement 1 is clearly insuff Statement 2 though xa=xb, so a/b = 1. Hence since the answer is positive, both need to be negative or both need to be positive. In any case a = b. I wonder what am I doing wrong here. Experts please advice Thank you Cheers There are two problems: 1. We cannot reduce xa=xb by x to get a=b. Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero. So when you divide by x you assume, with no ground for it, that x does not equal to zero thus exclude a possible solution. Notice that x=0 and a=b both satisfy xa=xb. 2. Even if we had a=b, it would still be insufficient. a=b means that a=b or a=b (consider a=b=1 and a=b=1). Hope it helps.
_________________
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



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6381
GPA: 3.82

Re: If ab ≠ 0, does a=b?
[#permalink]
Show Tags
17 Jan 2016, 22:37
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If ab ≠ 0, does a=b? (1) x^a = x^b (2) xa = xb In the original condition, there are 2 variables(a,b). But, overall, there are 3 variables(a,b,x), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, and you lack 1 equation, which is likely to make E the answer. When 1) & 2), if x=1, a=b=2 > yes, a=2, b=2 > no, which is not sufficient. Therefore, the answer is E. For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830

Re: If ab ≠ 0, does a=b?
[#permalink]
Show Tags
13 Jul 2018, 14:24
gmattokyo wrote: If ab ≠ 0, does a=b?
(1) x^a = x^b (2) xa = xb Since ab ≠ 0, that means neither a nor b is 0. We need to determine whether a = b. Statement One Alone: x^a = x^b If x = 2, then a = b. However, if x = 1, then a and b could be any numbers. For example, a could be 1 and b could be 2. Statement one alone is not sufficient. Statement Two Alone: xa = xb We see that a could equal b; for example, x = 1 and a = b = 1. However, a could also not equal b, for example, x = 1, a = 1 and b = 1. Statement two is not sufficient. Statements One and Two Together: With the two statements, we still can’t determine whether a = b. For example, x = 1 and a = b = 1 or x = 1, a = 1 and b = 1 and thus a does not equal b. Answer: E
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: If ab ≠ 0, does a=b? &nbs
[#permalink]
13 Jul 2018, 14:24






