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

It is currently 17 Feb 2019, 00:08

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 in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     February 17, 2019

     February 17, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Valentine's day SALE is on! 25% off.

     February 18, 2019

     February 18, 2019

     10:00 PM PST

     11:00 PM PST

    We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

In the equation x^2 + mx + n = 0, x is a variable and m and n are cons

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52902
In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 28 Aug 2017, 02:01
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (01:38) correct 34% (01:47) wrong based on 116 sessions

HideShow timer Statistics

In the equation x^2 + mx + n = 0, x is a variable and m and n are constants. What is the value of n ?

(1) x + 2 is a factor of x^2 + mx + n
(2) The equation x^2 + mx + n = 0 has only one root

_________________

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

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7334
Premium Member Reviews Badge
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 28 Aug 2017, 02:16
1
1
Bunuel wrote:
In the equation x^2 + mx + n = 0, x is a variable and m and n are constants. What is the value of n ?

(1) x + 2 is a factor of x2 + mx + n
(2) The equation x^2 + mx + n = 0 has only one root



hi..
Bunuel, typo in x2 + mx + n..

lets see the statements

(1) x + 2 is a factor of \(x^2 + mx + n\)
the equation has two roots and 'n' is the product of these TWO roots..
Only one -2 is known
Insuff


(2) The equation \(x^2 + mx + n = 0\) has only one root
this means \(n = root^2\)
insuff


combined

we know that the equation has one root and -2 is a root ..
so n= (-2)^2=4
sufficient
C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52902
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 28 Aug 2017, 02:21
chetan2u wrote:
Bunuel wrote:
In the equation x^2 + mx + n = 0, x is a variable and m and n are constants. What is the value of n ?

(1) x + 2 is a factor of x2 + mx + n
(2) The equation x^2 + mx + n = 0 has only one root



hi..
Bunuel, typo in x2 + mx + n..

lets see the statements

(1) x + 2 is a factor of \(x^2 + mx + n\)
the equation has two roots and 'n' is the product of these TWO roots..
Only one -2 is known
Insuff


(2) The equation \(x^2 + mx + n = 0\) has only one root
this means \(n = root^2\)
insuff


combined

we know that the equation has one root and -2 is a root ..
so n= (-2)^2=4
sufficient
C

___________________
Typo edited. 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

Current Student
User avatar
P
Joined: 18 Aug 2016
Posts: 623
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Premium Member Reviews Badge
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 28 Aug 2017, 02:29
Bunuel wrote:
In the equation x^2 + mx + n = 0, x is a variable and m and n are constants. What is the value of n ?

(1) x + 2 is a factor of x^2 + mx + n
(2) The equation x^2 + mx + n = 0 has only one root


(1) gives us x=-2 follows the equation
4-2m+n=0
n-2m=-4
one equation 2 variables
not sufficient

(2) only one root then m^2-4n=0
m^2 = 4n
one equation two variables
not sufficient

on combining
we have
n-2m=-4 & m^2 = 4n

can be solved to get the values of m & n
4n=16+8m=m^2
m^2-8m-16=0
m=4 and n=4
Also since n = r1*r2
but only one root i.e. -2
n=(-2)^2 = 4
C
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 458
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 28 Aug 2017, 02:35
2
Ans is C
see the pic for solution
Attachments

IMG_8225.JPG
IMG_8225.JPG [ 2.09 MiB | Viewed 4323 times ]


_________________

Give Kudos for correct answer and/or if you like the solution.

Manager
Manager
avatar
B
Joined: 20 Jun 2014
Posts: 51
GMAT 1: 630 Q49 V27
GMAT 2: 660 Q49 V32
Reviews Badge
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 29 Aug 2017, 04:48
(1) x + 2 is a factor of x^2 + mx + n

implies that x = -2
putting the value we get 4-2m+n = 0
insufficient

(2) The equation x^2 + mx + n = 0 has only one root
only one root implies that the roots are equal
for equal root = -b/2a
insufficient

combining 1 & 2
roots are equal and root is -2
so -b/2a = -2
=> -m/2 = -2
m = 4
and putting that value in equation from 1
4-2(4)+n =0
n=4
C is sufficient.
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 05 Sep 2017, 17:02
1
Bunuel wrote:
In the equation x^2 + mx + n = 0, x is a variable and m and n are constants. What is the value of n ?

(1) x + 2 is a factor of x^2 + mx + n
(2) The equation x^2 + mx + n = 0 has only one root


We need to determine the value of n.

Statement One Alone:

x + 2 is a factor of x^2 + mx + n.

Let f(x) = x^2 + mx + n. If x + 2 is a factor of x^2 + mx + n, then by the factor theorem, f(-2) = 0. That is, (-2)^2 + m(-2) + n = 0 or 4 - 2m + n = 0. However, since we don’t know the value of m, we can’t determine the value of n. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The equation x^2 + mx + n = 0 has only one root.

Let r be the root. Then we can express x^2 + mx + n as (x - r)^2:

x^2 + mx + n = (x - r)^2

x^2 + mx + n = x^2 - 2rx + r^2

We see that m = -2r and n = r^2. Since we don’t know the value of m or r, we can’t determine the value of n. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Since statement one states that x + 2 is a factor of x^2 + mx + n, x = -2 is a root of the equation x^2 + mx + nx = 0. Furthermore, since statement two states that there is only one root, x = -2 must be a double root. That is, x^2 + mx + n = (x + 2)^2:

x^2 + mx + n = (x + 2)^2

x^2 + mx + n = x^2 + 4x + 4

We see that m = 4 and n = 4.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
B
Joined: 27 Apr 2015
Posts: 41
GMAT 1: 370 Q29 V13
Reviews Badge
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 27 Dec 2017, 04:27
Bunuel wrote:
In the equation x^2 + mx + n = 0, x is a variable and m and n are constants. What is the value of n ?

(1) x + 2 is a factor of x^2 + mx + n
(2) The equation x^2 + mx + n = 0 has only one root


Given \(x^2+mx+n=0\) --- equ (1)

Find 'n'

Let r1 & r2 be the roots of the given Quadratic equation (1)
=> Now for a Standard Quad Equation of the form \(ax^2+bx+c=0\)
=> sum of the roots=\(\frac{-b}{a}\)

=> AND product of the roots=\(\frac{c}{a}\)

=> Therefore for equ (1) with roots r1 & r2
=> r1+r2=-m
=> AND r1*r2=n
so if we know the roots of the given equation we can find 'n'

Statement 1 (x + 2) is a factor of \(x^2 + mx + n\)
=> so (x+2)=0
=> OR x=-2= one of the roots
=> let r1=-2
=> Since r2 not known. Therefore Stat 1 NOT SUFFICIENT

Statement 2 The equation \(x^2 + mx + n = 0\) has only one root
=> so both the roots are equal
=> i.e r1=r2
=> n=\(r1^2\)=\(r2^2\)
=> since VALUE of the root not known. Therefore Stat2 NOT SUFFICIENT

BOTH Stat 1 & 2
=> r1=-2 from stat 1
=> n=\(r1^2\) from stat 2
=> Therefore n=\((-2)^2\)=4

Therefore 'C'

Thanks
Dinesh
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9836
Premium Member
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons  [#permalink]

Show Tags

New post 18 Jan 2019, 14:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: In the equation x^2 + mx + n = 0, x is a variable and m and n are cons   [#permalink] 18 Jan 2019, 14:04
Display posts from previous: Sort by

In the equation x^2 + mx + n = 0, x is a variable and m and n are cons

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


Copyright

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®.