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# In the equation x^2 + bx + 12 = 0, x is a variable and b is

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In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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29 Jan 2014, 01:14
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?

(1) x - 3 is a factor of x^2 + bx + 12.
(2) 4 is a root of the equation x^2 + bx + 12 = 0.

Data Sufficiency
Question: 62
Category: Algebra First- and second-degree equations
Page: 157
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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16 Jul 2017, 12:25
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1
In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?

(1)$$x - 3$$ is a factor of $$x^2 + bx + 12$$

as $$(x-3)$$ is one of the factor, this means that $$x = 3$$ is one of the roots of the equation $$x^2 + bx + 12$$

In order to get 12 = we only have one value after 3 and that is 4 as $$4 * 3 = 12$$

Hence, $$bx = 4x + 3x = 7x$$, value of $$b = 7$$

Hence, (1) ===== is SUFFICIENT

(2) 4 is a root of the equation $$x^2 + bx + 12 = 0$$

As 4 is one of the roots, the other root will be 3

Hence, $$bx = 4x + 3x = 7x$$, value of $$b = 7$$

Hence, (2) ===== is SUFFICIENT

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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29 Jan 2014, 01:15
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SOLUTION

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?[b][/b]

(1) x-3 is a factor of x^2 + bx + 12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2 + bx + 12 = 0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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29 Jan 2014, 01:51
From S1:x-3 is a factor of the given equation=>x=3 is a root of the equation.Putting x=3 in the eq x^2+bx+12 we can get the value of b.Hence sufficient.
From S2:4 is a root of the equation=>Putting x=4 in the equation we can find out b.Sufficient.
Ans.D
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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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03 Jan 2018, 08:10
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?

(1) x - 3 is a factor of x^2 + bx + 12.
(2) 4 is a root of the equation x^2 + bx + 12 = 0.

Data Sufficiency
Question: 62
Category: Algebra First- and second-degree equations
Page: 157
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

From st 1: x - 3 is a factor of x^2 + bx + 12

x - 3 = 0 or x = 3

Put x = 3 in x^2 + bx + 12 = 0. This gives us x = -7 -----> Sufficient

From st 2: 4 is a root of the equation x^2 + bx + 12 = 0

means x = 4,

Put x = 4 in x^2 + bx + 12 = 0. This gives us x = -7 ------> Sufficient

(D)
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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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10 Jun 2018, 10:13
Bunuel wrote:
SOLUTION

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?[b][/b]

(1) x-3 is a factor of x^2 + bx + 12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2 + bx + 12 = 0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

I'm a bit confused as to the term 'root' and specifically the phrase '4 is a root of x^2' here. How should this be interpreted?

I thought of it as the factor of 12 (i.e. 4x = 12).

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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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10 Jun 2018, 10:18
Top Contributor
1
energy2pe wrote:
Bunuel wrote:
SOLUTION

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?[b][/b]

(1) x-3 is a factor of x^2 + bx + 12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2 + bx + 12 = 0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

I'm a bit confused as to the term 'root' and specifically the phrase '4 is a root of x^2' here. How should this be interpreted?

I thought of it as the factor of 12 (i.e. 4x = 12).

"root" is the same as "solution"

We can say "x = 3 is a solution to the equation 2x = 6" or we can say "3 is a root of the equation 2x = 6"

Cheers,
Brent
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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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10 Jun 2018, 10:32
GMATPrepNow wrote:
energy2pe wrote:
Bunuel wrote:
SOLUTION

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?[b][/b]

(1) x-3 is a factor of x^2 + bx + 12 --> simply means that x=3 is a root of x^2+bx+12=0 (if x-3 is a factor of x^2+bx+12 then x^2+bx+12=(x-3)(x-k)=0, for some k, so x=3 is on of the roots of the equation) --> substitute x=3: 3^2+3b+12=0 --> b=-7. Sufficient.

(2) 4 is a root of x^2 + bx + 12 = 0 --> the same here, substitute x=4: 4^2+4b+12=0 --> b=-7. Sufficient.

I'm a bit confused as to the term 'root' and specifically the phrase '4 is a root of x^2' here. How should this be interpreted?

I thought of it as the factor of 12 (i.e. 4x = 12).

"root" is the same as "solution"

We can say "x = 3 is a solution to the equation 2x = 6" or we can say "3 is a root of the equation 2x = 6"

Cheers,
Brent

Ahh, got it. Thanks.

Fan of the youtube channel btw--I've subscribed : )
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Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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17 Jun 2019, 07:00
In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?

(1)x−3x−3 is a factor of x2+bx+12x2+bx+12

as (x−3)(x−3) is one of the factor, this means that x=3x=3 is one of the roots of the equation x2+bx+12x2+bx+12

In order to get 12 = we only have one value after 3 and that is 4 as 4∗3=124∗3=12

Hence, bx=4x+3x=7xbx=4x+3x=7x, value of b=7b=7

Hence, (1) ===== is SUFFICIENT

(2) 4 is a root of the equation x2+bx+12=0x2+bx+12=0

As 4 is one of the roots, the other root will be 3

Hence, bx=4x+3x=7xbx=4x+3x=7x, value of b=7b=7

Hence, (2) ===== is SUFFICIENT

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In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

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16 Sep 2019, 01:57
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant. What is the value of b ?

(1) x - 3 is a factor of x^2 + bx + 12.
(2) 4 is a root of the equation x^2 + bx + 12 = 0.

Data Sufficiency
Question: 62
Category: Algebra First- and second-degree equations
Page: 157
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Given: In the equation x^2 + bx + 12 = 0, x is a variable and b is a constant.

Asked: What is the value of b ?

(1) x - 3 is a factor of x^2 + bx + 12.
9+3b+12 = 0
b = -7
SUFFICIENT

(2) 4 is a root of the equation x^2 + bx + 12 = 0.
16 + 4b + 12 = 0
b = - 7
SUFFICIENT

IMO D
In the equation x^2 + bx + 12 = 0, x is a variable and b is   [#permalink] 16 Sep 2019, 01:57
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