NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 00:11 It is currently 26 Apr 2024, 00:11
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If ab ≠ 0, does a = b?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92916
Own Kudos [?]: 619079 [20]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
If ab ≠ 0, does a = b? [#permalink] New post   01 Apr 2016, 03:30
4
Kudos
16
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

62% (01:19) correct 38% (01:07) wrong based on 523 sessions
Hide Show timer Statistics
If ab ≠ 0, does a = b?

(1) x^a = x^b
(2) x = x^2
ShowHide Answer
Official Answer
E
User avatar
D
Kurtosis
Current Student
Joined: 13 Apr 2015
Posts: 1436
Own Kudos [?]: 4548 [0]
Given Kudos: 1228
Location: India
Send PM
GMAT ToolKit User Reviews Badge
Re: If ab ≠ 0, does a = b? [#permalink] New post   01 Apr 2016, 03:50
Is a = b?

St1: x^a = x^b
If x = 1 then 1^2 = 1^3 --> Is a = b? No
If x > 1; 2^2 = 2^2 --> Is a = b? Yes
Not Sufficient

St2: x = x^2 --> Provides information that x = 0 or x = 1. No information about a and b. Not Sufficient

Combining St1 and St2;
1^2 = 1^2 --> Is a = b? Yes
1^2 = 1^3 --> Is a = b? No
Not sufficient.

Answer: E
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16598 [2]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: If ab ≠ 0, does a = b? [#permalink] New post   03 Apr 2016, 04:28
2
Bookmarks
Expert Reply
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) x = x^2


In the original condition, there are 3 variables(x,a,b), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, and 1 more equation is needed, which is likely to make E the answer.
When 1) & 2), if x=1, a=b=1 -> yes. If x=1, a=1, b=2, it is no and not sufficient.
Thus, 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.
User avatar
L
billionaire
Retired Moderator
Joined: 21 Mar 2018
Posts: 492
Own Kudos [?]: 501 [0]
Given Kudos: 72
Concentration: Finance
Send PM
If ab ≠ 0, does a = b? [#permalink] New post   24 Mar 2018, 23:24
Bunuel wrote:
If ab ≠ 0, does a = b?

(1) x^a = x^b
(2) x = x^2



we have both possibilities a could equal b but not necessarily...we can see that x=1 because only 1=1^2....now if we know that x=1 then a and be can be any positive integers and condition x^a = x^b will still be satisfied...and they can also be equal to each other....of course x can be zero and then again both cases are possible same as for x=1, a and b can or not be equal
avatar
B
joneson
Intern
Intern
Joined: 30 Jan 2018
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 6
Send PM
If ab ≠ 0, does a = b? [#permalink] New post   Updated on: 04 Apr 2018, 05:14
Statement 1 states:

x^a=x^b
Why can we not get rid of the base x, as it is the same on both sides and say a=b?

Edit: Bunuel you are a GMAT Angel! <3

Originally posted by joneson on 04 Apr 2018, 02:05.
Last edited by joneson on 04 Apr 2018, 05:14, edited 1 time in total.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92916
Own Kudos [?]: 619079 [2]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If ab ≠ 0, does a = b? [#permalink] New post   04 Apr 2018, 05:03
2
Kudos
Expert Reply
joneson wrote:
Statement 1 states:

x^a=x^b
Why can we not get rid of the base x, as it is the same on both sides and say a=b?


Remember we can automatically equate the exponents of equal bases when that base does not equal 0, 1 or -1:

\(1^a = 1^b\), for any values of a and b (they are not necessarily equal);
\((-1)^a = (-1)^b\), for any even values of a and b (they are not necessarily equal);
\(0^a = 0^b\), for any non-zero a and b (they are not necessarily equal).
User avatar
B
coolo
Intern
Intern
Joined: 26 Jan 2018
Posts: 11
Own Kudos [?]: 3 [0]
Given Kudos: 0
Send PM
Why "Solving Exponential Equations with the Same Base" does not hold? [#permalink] New post   24 Apr 2018, 12:48
This question has been discussed before on the forums but I do not understand why the "Solving Exponential Equations with the Same Base" rule does not hold in this follow example:

If ab ≠ 0, does a=b?

(1) x^a = x^b
(2) x = x^2

______________________________

RULE: Solving Exponential Equations with the Same Base: If B^M = B^N, then M = N.

FOR STATEMENT #1 Why doesn't this rule hold???? I understand if you set x=1, a=2, b=2 then a=b BUT if you set x=1, a=2, b=-2 then a≠b . I am trying to understand the logic why the above RULE doesn't apply in this particular case??

FYI: The solution to this problem according to the answer key is E based on the "plug-in numbers" technique described above.

Thanks for the help!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92916
Own Kudos [?]: 619079 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If ab ≠ 0, does a = b? [#permalink] New post   24 Apr 2018, 13:00
Expert Reply
coolo wrote:
This question has been discussed before on the forums but I do not understand why the "Solving Exponential Equations with the Same Base" rule does not hold in this follow example:

If ab ≠ 0, does a=b?

(1) x^a = x^b
(2) x = x^2

______________________________

RULE: Solving Exponential Equations with the Same Base: If B^M = B^N, then M = N.

FOR STATEMENT #1 Why doesn't this rule hold???? I understand if you set x=1, a=2, b=2 then a=b BUT if you set x=1, a=2, b=-2 then a≠b . I am trying to understand the logic why the above RULE doesn't apply in this particular case??

FYI: The solution to this problem according to the answer key is E based on the "plug-in numbers" technique described above.

Thanks for the help!


Your doubt is addressed here: https://gmatclub.com/forum/if-ab-0-does ... l#p2040836
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6820
Own Kudos [?]: 29936 [0]
Given Kudos: 799
Location: Canada
Send PM
If ab ≠ 0, does a = b? [#permalink] New post   Updated on: 28 May 2020, 09:28
Expert Reply
Top Contributor
coolo wrote:
RULE: Solving Exponential Equations with the Same Base: If B^M = B^N, then M = N.


Your rule (above) requires some provisos.

For example, if 0^M = 0^N, we can't necessarily conclude that M = N
Likewise, if 1^M = 1^N, we can't necessarily conclude that M = N
Likewise, if 1^M = (-1)^N, we can't necessarily conclude that M = N. For example, M = 1 and N = 2 satisfies the given equation, but M ≠ N

Originally posted by BrentGMATPrepNow on 24 Apr 2018, 13:07.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:28, edited 1 time in total.
avatar
B
seed
Manager
Manager
Joined: 03 Oct 2016
Posts: 98
Own Kudos [?]: 151 [0]
Given Kudos: 64
Send PM
If ab ≠ 0, does a = b? [#permalink] New post   24 Apr 2018, 14:04
Bunuel wrote:
If ab ≠ 0, does a = b?

(1) x^a = x^b
(2) x = x^2



1) x^a=x^b -> x^a/x^b=1 -> x^(a-b)=1^1=1^0. Now, a-b=1 -> a ≠ b (No) and a-b=0 -> a = b (Yes). Not sufficient.
2) x = x^2 - Not sufficient as we don't know about a and b.

1)+2) putting x=x^2 in 1)
x^2a=x^2b -> x^2a/x^2b -> x^(2a-2b)=1^1=1^0, so 2a-2b=1 -> a ≠ b (No) and 2a-2b=0 -> a=b (Yes)

Together not sufficient.

Answer: (E).
User avatar
P
push12345
Director
Director
Joined: 02 Oct 2017
Posts: 552
Own Kudos [?]: 481 [0]
Given Kudos: 14
Send PM
Re: If ab ≠ 0, does a = b? [#permalink] New post   12 May 2018, 05:58
I) x^a=x^b
If x=zero
Then equation holds but we can't say whether a=b or not
Both cases hold
So insufficient

II) x^2-x=0
x(x-1)=0
x=0 or x=1
Insufficient as no info about a And b

Combining both
X can be zero or 1 in either case
Equation holds and a and b can have any value without changing result of equation so not sufficient
E is answer

Give kudos if it helps

Posted from my mobile device
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32680
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If ab 0, does a = b? [#permalink] New post   06 Dec 2023, 09:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If ab 0, does a = b? [#permalink]
06 Dec 2023, 09:55
Moderator:
Bunuel
Math Expert
92915 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions