GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jan 2019, 21:38

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

# If ab ≠ 0, does a = b?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52297
If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

01 Apr 2016, 02:30
3
5
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:17) correct 42% (01:04) wrong based on 248 sessions

### HideShow timer Statistics

If ab ≠ 0, does a = b?

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

_________________
SC Moderator
Joined: 13 Apr 2015
Posts: 1687
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

01 Apr 2016, 02:50
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.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6821
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

03 Apr 2016, 03:28
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.

 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 one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Admitted - Which School Forum Moderator
Joined: 21 Mar 2018
Posts: 322
Concentration: Finance
If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

24 Mar 2018, 22:24
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
_________________

Intern
Joined: 30 Jan 2018
Posts: 1
If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

Updated on: 04 Apr 2018, 04:14
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, 01:05.
Last edited by joneson on 04 Apr 2018, 04:14, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 52297
Re: If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

04 Apr 2018, 04:03
1
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).
_________________
Intern
Joined: 26 Jan 2018
Posts: 12
Why "Solving Exponential Equations with the Same Base" does not hold?  [#permalink]

### Show Tags

24 Apr 2018, 11:48
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!
Math Expert
Joined: 02 Sep 2009
Posts: 52297
Re: If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

24 Apr 2018, 12:00
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!

_________________
CEO
Joined: 11 Sep 2015
Posts: 3344
Re: Why "Solving Exponential Equations with the Same Base" does not hold?  [#permalink]

### Show Tags

24 Apr 2018, 12:07
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

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com

Manager
Joined: 03 Oct 2016
Posts: 126
If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

24 Apr 2018, 13:04
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.

_________________

Non-Allergic To Kudos

Director
Joined: 02 Oct 2017
Posts: 735
Re: If ab ≠ 0, does a = b?  [#permalink]

### Show Tags

12 May 2018, 04:58
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

Give kudos if it helps

Posted from my mobile device
_________________

Give kudos if you like the post

Re: If ab ≠ 0, does a = b? &nbs [#permalink] 12 May 2018, 04:58
Display posts from previous: Sort by