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

 It is currently 22 Feb 2020, 01:13 ### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61385
In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

19 00:00

Difficulty:   5% (low)

Question Stats: 81% (01:10) correct 19% (01:37) wrong based on 865 sessions

### HideShow timer Statistics

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!

_________________
Retired Moderator P
Joined: 19 Mar 2014
Posts: 912
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

5
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

Did you like the answer? 1 Kudos Please _________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 61385
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

4
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.

_________________
Manager  Joined: 20 Dec 2013
Posts: 220
Location: India
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

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
SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1698
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

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)
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Consortium Forum Moderator S
Joined: 11 Mar 2018
Posts: 87
Location: United States
GMAT 1: 690 Q48 V37
GMAT 2: 710 Q47 V41
GPA: 3.6
WE: Analyst (Energy and Utilities)
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

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).

_________________
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4337
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

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
_________________
Consortium Forum Moderator S
Joined: 11 Mar 2018
Posts: 87
Location: United States
GMAT 1: 690 Q48 V37
GMAT 2: 710 Q47 V41
GPA: 3.6
WE: Analyst (Energy and Utilities)
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

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 : )
_________________
Manager  B
Joined: 03 Jun 2017
Posts: 108
Location: India
Concentration: Strategy, Operations
GMAT 1: 500 Q39 V20
GPA: 3.82
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

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

SVP  D
Joined: 03 Jun 2019
Posts: 2013
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
In the equation x^2 + bx + 12 = 0, x is a variable and b is  [#permalink]

### Show Tags

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
Display posts from previous: Sort by

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