GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 04 Apr 2020, 14:02

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.

Close

Request Expert Reply

Confirm Cancel

Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62499
Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 00:48
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

64% (01:10) correct 36% (01:07) wrong based on 84 sessions

HideShow timer Statistics

Manager
Manager
avatar
S
Joined: 30 Nov 2017
Posts: 66
GMAT 1: 690 Q49 V35
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 00:57
1
Does a=0?

(1) a3(8.12)=a4(8.12)
Solving above either a=0 or a=1. Insufficient.

(2) ab≠b
From above one thing is sure i.e. a ≠ 1 but a can be any other number satisfying this eq. Insufficient.

Combining, we know a=0. Ans C.
SVP
SVP
avatar
V
Joined: 20 Jul 2017
Posts: 1519
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 01:23
2
(1) \(a^3(8.12) = a^4(8.12)\)
--> \(a^4(8.12) - a^3(8.12) = 0\)
--> \(a^3(8.12)(a - 1) = 0\)
--> \(a^3(a - 1) = 0\)
--> a = 0 or a = 1 --> Insufficient

(2) \(ab ≠ b\)
--> \(ab - b ≠ 0\)
--> \(b(a - 1) ≠ 0\)
--> b ≠ 0 or a ≠ 1
--> '\(a\)' can take any value other than 1 --> Insufficient

Combining (1) & (2),
Since \(a ≠ 1\) --> \(a = 0\) ONLY --> Sufficient

IMO Option C
Director
Director
User avatar
D
Joined: 07 Mar 2019
Posts: 911
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 01:50
1
Does a = 0?

(1) \(a^3(8.12) = a^4(8.12)\)
\(a^3 = a^4\)
\(a^4 - a^3 = 0\)
\(a (a^3 - a) = 0\)
So, a = 0 or a = 1

INSUFFICIENT.

(2) ab ≠ b
Take a = 1 and b = 2
Thus,
ab = 1 * 2 = 2
But since ab = b = 2, a ≠ 1
However, a can be equal to 0, 2, 3 .... so on.

INSUFFICIENT.

Together 1 and 2
As a ≠ 1 , so a = 0

SUFFICIENT.

IMO Answer C.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1349
Location: United States
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 03:08
1
Quote:
Does a=0?

(1) \(a^3(8.12)=a^4(8.12)\)
(2) ab≠b


(1) \(a^3(8.12)=a^4(8.12)\) insufic

\(a^3x=a^4x…a=0:0x=0x…0=0=true\)
\(a^3x=a^4x…a=1:1x=1x…x=x=true\)

(2) ab≠b insufic

\(a≠1,b≠0\)

(1 & 2) sufic

\(a≠1,b≠0…a=0\)

Ans (C)
Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 491
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GMAT 1: 580 Q48 V21
GPA: 4
Reviews Badge
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 04:28
1
(1) a^3(8.12) = a^4(8.12)
a^3(8.12)(a-1)=0
So either a=0 or a=1.... insufficient
(2) ab not equal to b
Then a can be anything other than 1....so insufficient

Combining both we get a=0 is the common value


OA:C

Posted from my mobile device
CR Forum Moderator
avatar
P
Joined: 18 May 2019
Posts: 788
GMAT ToolKit User Premium Member
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 06:42
1
Does a=0?

Statement 1: a^3(8.12)=a^4(8.12)
from statement 1, we know that a^3(1-a)=0
hence a=0 and a=1.
but since a=0 and a=1, then statement 1 is not sufficient since we have Yes and No answers to the question posed.

(2) ab≠b
from statement 2, we know that a≠1
But a can be 0 since 0*b=0 and 0≠b, the condition in statement 2 is satisfied. When a=0, then the answer is Yes to the question asked.
when a=2, the ab=2b and 2b≠b, hence statement 2 is satisfied.
But a≠0, hence the answer this time around is No.

1+2
From statement 1, we know that a=0 and a=1
but statement 2 says a≠1, and a can take any other value apart from 1. Meanwhile statement 1 also limits the possible values of a to 0 and 1, and since a≠1, then a=0.
So the answer to the above question is Yes, a=0.

Statements 1 and 2 taken together are therefore sufficient.

The answer is option C in my view.
Senior Manager
Senior Manager
User avatar
P
Joined: 10 Apr 2018
Posts: 310
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34
GPA: 3.3
Reviews Badge
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 07:59
1
Quote:
Does a=0a=0?

(1) a3(8.12)=a4(8.12)a3(8.12)=a4(8.12)
(2) ab≠b


(1) a^3-a^4=0
=> a^3(1-a)=0
=> a=0 or 1
Thus, this statement is insufficient.

(2) From this statement, we get that a≠1, so a can be any number but 1.
Thus, this statement is insufficient.

From (1) and (2), we get that a=0.
Therefore, correct answer is option C.
Current Student
User avatar
G
Joined: 11 Feb 2013
Posts: 266
Location: United States (TX)
Schools: Neeley '21 (A$)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
GMAT ToolKit User Premium Member Reviews Badge
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 08:45
I would go for C.

Is a=0?
Statement 1: a=0 (yes) or a=1 (no)
Statement 2: a is Not equal 1. So a can be any integer except 1.
a=0 (yes) or a=5 (no)

Combining:
statement 1: a=0 or a=1
Statement 2: a can not be 1
So a must be zero.
SUFFICIENT.
Current Student
User avatar
G
Joined: 11 Feb 2013
Posts: 266
Location: United States (TX)
Schools: Neeley '21 (A$)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
GMAT ToolKit User Premium Member Reviews Badge
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 08:46
I would go for C.

Is a=0?
Statement 1: a=0 (yes) or a=1 (no)
Statement 2: a is Not equal 1. So a can be any integer except 1.
a=0 (yes) or a=5 (no)

Combining:
statement 1: a=0 or a=1
Statement 2: a can not be 1
So a must be zero.
SUFFICIENT.
Intern
Intern
avatar
B
Joined: 12 Aug 2019
Posts: 21
Location: India
Concentration: Finance, Leadership
GMAT 1: 700 Q49 V35
GPA: 4
WE: Account Management (Retail Banking)
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 09:10
1
C as combining the two will give a definitive answer. First options tells a is 0 or 1. Second alone tells a can have multiple values but 1. Combine the two and so a is 0

Posted from my mobile device
Senior Manager
Senior Manager
avatar
G
Joined: 23 Nov 2018
Posts: 254
GMAT 1: 650 Q49 V28
GPA: 4
Reviews Badge
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 08 Nov 2019, 23:19
1
Does a=0?

(1) a^3*(8.12)=a^4*(8.12)

a^3*8.12(1-a)=0

a*(1-a)=0

a=1 or a=0---- insufficient

(2) ab≠b

b(a-1)≠0

b≠ a≠1

a=0 yes; a=2 No


therefore C is sufficent
_________________
.
Director
Director
avatar
D
Joined: 22 Feb 2018
Posts: 598
GMAT ToolKit User CAT Tests
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 09 Nov 2019, 01:12
Does a=0?

(1) a3(8.12)=a4(8.12)
a3=a4, a = 0 or 1, Insufficient.

(2) ab≠b, If a = 0 and b = 1, ab≠b. If a = 1 and b = 0, ab≠b, Still a can be 0 or 1. Insufficient.

1) + 2) a can be 0 or 1. Insufficient.

Imo. E.
Manager
Manager
avatar
G
Joined: 11 Mar 2018
Posts: 173
GMAT ToolKit User
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 09 Nov 2019, 19:35
IMO D

We need to find if a = 0 ?

Statement - 1: \(a^3(8.12) = a^4(8.12)\)
=> \(a^3 = a^4\)
=> \(a^4 - a^3 = 0\)
=> \(a^3(a - 1) = 0\)
=> either a = 0 or a = 1

Hence Insufficient

Statement - 2: \(ab ≠ b\)
=> a ≠ 1,

Hence Insufficient

Combining Statements 1 and 2,
Combining we know that 'a' can only be '0'.

Hence sufficient
_________________
Regards,
AD
----------------

An admiration by anybody is an explanation understood by somebody !!!

Happy GMATing... Go Nuts :)
Manager
Manager
User avatar
B
Status: No knowledge goes waste
Joined: 12 Jul 2019
Posts: 69
Location: Norway
Concentration: Finance, Accounting
GPA: 3
WE: Corporate Finance (Commercial Banking)
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 10 Nov 2019, 19:24
got it wrong, waiting for explanation.
Intern
Intern
avatar
B
Joined: 25 Feb 2019
Posts: 28
GMAT 1: 520 Q43 V20
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 11 Nov 2019, 19:34
Could someone explain when we have a^3 = a^4 why is a =1 not the solution? In gmat is it that we have to move the terms from right to the left to make the equation equal to zero always? Just curious to know the reasoning behind this.

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 30 Nov 2017
Posts: 66
GMAT 1: 690 Q49 V35
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 11 Nov 2019, 19:45
porwal1 wrote:
Could someone explain when we have a^3 = a^4 why is a =1 not the solution? In gmat is it that we have to move the terms from right to the left to make the equation equal to zero always? Just curious to know the reasoning behind this.

Posted from my mobile device


It’s not gmat thing. It’s maths! basically it’s a method to find all the solutions of a equation.

Further to answer your question, a=1is a solution but also a=0. Both the values satisfies the equation. And only by solving this equation you will be able to find all the solution.
Intern
Intern
avatar
B
Joined: 25 Feb 2019
Posts: 28
GMAT 1: 520 Q43 V20
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

Show Tags

New post 11 Nov 2019, 19:51
vg18 wrote:
porwal1 wrote:
Could someone explain when we have a^3 = a^4 why is a =1 not the solution? In gmat is it that we have to move the terms from right to the left to make the equation equal to zero always? Just curious to know the reasoning behind this.

Posted from my mobile device


It’s not gmat thing. It’s maths! basically it’s a method to find all the solutions of a equation.

Further to answer your question, a=1is a solution but also a=0. Both the values satisfies the equation. And only by solving this equation you will be able to find all the solution.


Thanks vg18 its just sometimes i tend to divide a^4 and a^3 which ends up with one solution a=1.
GMAT Club Bot
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b   [#permalink] 11 Nov 2019, 19:51
Display posts from previous: Sort by

Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne