GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Jun 2018, 12:32

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46264
In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

Show Tags

New post 29 Jan 2014, 02:14
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

81% (00:52) correct 19% (01:05) wrong based on 516 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:
1. Please provide your solutions to the questions;
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!

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46264
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

Show Tags

New post 29 Jan 2014, 02:15
2
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.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 250
Location: India
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

Show Tags

New post 29 Jan 2014, 02:51
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
2 KUDOS received
Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 974
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

Show Tags

New post 16 Jul 2017, 13:25
2
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

Hence, Answer is D

Did you like the answer? 1 Kudos Please :good
_________________

"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

VP
VP
User avatar
D
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1051
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

Show Tags

New post 03 Jan 2018, 09:10
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:
1. Please provide your solutions to the questions;
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)
_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Intern
Intern
avatar
B
Joined: 11 Mar 2018
Posts: 4
WE: Analyst (Consulting)
Premium Member
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

Show Tags

New post 10 Jun 2018, 11:13
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.

Answer: D.


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).

Thanks ahead of time.
Expert Post
Top Contributor
CEO
CEO
User avatar
P
Joined: 12 Sep 2015
Posts: 2567
Location: Canada
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

Show Tags

New post 10 Jun 2018, 11:18
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.

Answer: D.


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).

Thanks ahead of time.


"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
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Intern
Intern
avatar
B
Joined: 11 Mar 2018
Posts: 4
WE: Analyst (Consulting)
Premium Member
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is [#permalink]

Show Tags

New post 10 Jun 2018, 11:32
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.

Answer: D.


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).

Thanks ahead of time.


"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 : )
Re: In the equation x^2 + bx + 12 = 0, x is a variable and b is   [#permalink] 10 Jun 2018, 11:32
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.