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

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

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08 Nov 2019, 01:48
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Does $$a = 0$$?

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

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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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08 Nov 2019, 01:57
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.
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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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08 Nov 2019, 02:23
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
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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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08 Nov 2019, 02:50
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.

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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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08 Nov 2019, 04:08
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)
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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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08 Nov 2019, 05:28
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

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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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08 Nov 2019, 07:42
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.
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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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08 Nov 2019, 08:59
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.
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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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08 Nov 2019, 09:45
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.
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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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08 Nov 2019, 09:46
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.
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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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08 Nov 2019, 10:10
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

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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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09 Nov 2019, 00:19
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
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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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09 Nov 2019, 02:12
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.
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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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09 Nov 2019, 20:35
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
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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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10 Nov 2019, 20:24
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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11 Nov 2019, 20:34
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.

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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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11 Nov 2019, 20:45
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.

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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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11 Nov 2019, 20:51
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, 20:51
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