Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62499

Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
08 Nov 2019, 00:48
Question Stats:
64% (01:10) correct 36% (01:07) wrong based on 84 sessions
HideShow timer Statistics
Competition Mode Question Does \(a = 0\)? (1) \(a^3(8.12) = a^4(8.12)\) (2) \(ab ≠ b\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Manager
Joined: 30 Nov 2017
Posts: 66

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
08 Nov 2019, 00:57
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
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
08 Nov 2019, 01:23
(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
Joined: 07 Mar 2019
Posts: 911
Location: India
WE: Sales (Energy and Utilities)

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
08 Nov 2019, 01:50
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
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
08 Nov 2019, 03:08
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
Joined: 01 Mar 2019
Posts: 491
Location: India
Concentration: Strategy, Social Entrepreneurship
GPA: 4

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
08 Nov 2019, 04:28
(1) a^3(8.12) = a^4(8.12) a^3(8.12)(a1)=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
Joined: 18 May 2019
Posts: 788

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
08 Nov 2019, 06:42
Does a=0?
Statement 1: a^3(8.12)=a^4(8.12) from statement 1, we know that a^3(1a)=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
Joined: 10 Apr 2018
Posts: 310
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34
GPA: 3.3

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
08 Nov 2019, 07:59
Quote: Does a=0a=0?
(1) a3(8.12)=a4(8.12)a3(8.12)=a4(8.12) (2) ab≠b (1) a^3a^4=0 => a^3(1a)=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
Joined: 11 Feb 2013
Posts: 266
Location: United States (TX)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
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
Joined: 11 Feb 2013
Posts: 266
Location: United States (TX)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
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
Joined: 12 Aug 2019
Posts: 21
Location: India
Concentration: Finance, Leadership
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
08 Nov 2019, 09:10
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
Joined: 23 Nov 2018
Posts: 254
GMAT 1: 650 Q49 V28
GPA: 4

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
08 Nov 2019, 23:19
Does a=0? (1) a^3*(8.12)=a^4*(8.12) a^3*8.12(1a)=0 a*(1a)=0 a=1 or a=0 insufficient (2) ab≠b b(a1)≠0 b≠ a≠1 a=0 yes; a=2 No therefore C is sufficent
_________________



Director
Joined: 22 Feb 2018
Posts: 598

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
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
Joined: 11 Mar 2018
Posts: 173

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
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 = 1Hence InsufficientStatement  2: \(ab ≠ b\)=> a ≠ 1,Hence InsufficientCombining 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
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
10 Nov 2019, 19:24
got it wrong, waiting for explanation.



Intern
Joined: 25 Feb 2019
Posts: 28

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
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
Joined: 30 Nov 2017
Posts: 66

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
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
Joined: 25 Feb 2019
Posts: 28

Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
Show Tags
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.




Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b
[#permalink]
11 Nov 2019, 19:51






