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Math Expert V
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Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

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

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Competition Mode Question

Does $$a = 0$$?

(1) $$a^3(8.12) = a^4(8.12)$$
(2) $$ab ≠ b$$

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

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

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

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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.

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

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

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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

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

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

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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.
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Joined: 11 Feb 2013
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Schools: Neeley '21 (A$) GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38 GPA: 3.05 WE: Analyst (Commercial Banking) Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b [#permalink] ### Show Tags I would go for C. Is a=0? Statement 1: a=0 (yes) or a=1 (no) Statement 2: a is Not equal 1. So a can be any integer except 1. a=0 (yes) or a=5 (no) Combining: statement 1: a=0 or a=1 Statement 2: a can not be 1 So a must be zero. SUFFICIENT. Current Student G Joined: 11 Feb 2013 Posts: 266 Location: United States (TX) Schools: Neeley '21 (A$)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38 GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

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

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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

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

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

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

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

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got it wrong, waiting for explanation.
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Re: Does a = 0? (1) a^3(8.12) = a^4(8.12) (2) ab ≠ b  [#permalink]

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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.

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

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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.

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

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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
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