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

It is currently 21 Sep 2018, 06:55

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

If q is one root of the equation x^2 + 18x + 11c = 0, where

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

Hide Tags

Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 833
GMAT ToolKit User
If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post Updated on: 24 Oct 2012, 05:02
3
10
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:32) correct 33% (01:42) wrong based on 326 sessions

HideShow timer Statistics

If q is one root of the equation x^2 + 18x + 11c = 0, where –11 is the other root and c is a constant, then q^2-c^2 =

A) 98
B) 72
C) 49
D) 0
E) It can't be determined from the information given

Originally posted by LM on 24 Oct 2012, 04:43.
Last edited by Bunuel on 24 Oct 2012, 05:02, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: Quadratic Equation Root  [#permalink]

Show Tags

New post 24 Oct 2012, 05:08
1
8
LM wrote:
If q is one root of the equation \(x^2 + 18x + 11c = 0\), where –11 is the other root and c is a constant, then \((q^2)-(c^2) =\)

A) 98
B) 72
C) 49
D) 0
E) It can't be determined from the information given


Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).


Thus according to the above \(x_1+x_2=q+(-11)=\frac{-18}{1}\) --> \(q=-7\) AND \(x_1*x_2=(-7)*(-11)=\frac{11c}{1}\) --> \(c=7\).

\(q^2-c^2 =(-7)^2-7^2=0\).

Answer: D.

Hope it's clear.
_________________

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

General Discussion
Intern
Intern
avatar
Status: wants to beat the gmat
Joined: 18 Jul 2012
Posts: 19
Location: United States
Re: Quadratic Equation Root  [#permalink]

Show Tags

New post 24 Oct 2012, 15:24
1
Bunuel wrote:
LM wrote:
If q is one root of the equation \(x^2 + 18x + 11c = 0\), where –11 is the other root and c is a constant, then \((q^2)-(c^2) =\)

A) 98
B) 72
C) 49
D) 0
E) It can't be determined from the information given


Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).


Thus according to the above \(x_1+x_2=q+(-11)=\frac{-18}{1}\) --> \(q=7\) AND \(x_1*x_2=7*(-11)=\frac{11c}{1}\) --> \(c=-7\).

\(q^2-c^2 =7^2-(-7)^2=0\).

Answer: D.

Hope it's clear.



shouldn't q = -7 and c = 7?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: Quadratic Equation Root  [#permalink]

Show Tags

New post 24 Oct 2012, 17:09
watwazdaquestion wrote:
Bunuel wrote:
LM wrote:
If q is one root of the equation \(x^2 + 18x + 11c = 0\), where –11 is the other root and c is a constant, then \((q^2)-(c^2) =\)

A) 98
B) 72
C) 49
D) 0
E) It can't be determined from the information given


Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).


Thus according to the above \(x_1+x_2=q+(-11)=\frac{-18}{1}\) --> \(q=7\) AND \(x_1*x_2=7*(-11)=\frac{11c}{1}\) --> \(c=-7\).

\(q^2-c^2 =7^2-(-7)^2=0\).

Answer: D.

Hope it's clear.



shouldn't q = -7 and c = 7?


Sure. Typo edited. Thank you. +1.
_________________

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

Intern
Intern
avatar
Joined: 16 Jan 2014
Posts: 44
Re: If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post 15 Sep 2014, 14:19
The way I approached this question is as follows:

1) If one root is -11 then using the rule of factoring: (x+11)(x+7)=0, q=-7, c=7
2) Since q^2-c^2=(q+c)(q-c), (q+c)=-7+7=0, q^2-c^2=0
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8283
Location: Pune, India
Re: If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post 15 Sep 2014, 22:09
2
LM wrote:
If q is one root of the equation x^2 + 18x + 11c = 0, where –11 is the other root and c is a constant, then q^2-c^2 =

A) 98
B) 72
C) 49
D) 0
E) It can't be determined from the information given


Another method to solve it is - plug the root that is available to get the value of c.

\((-11)^2 + 18*(-11) + 11c = 0\)
\(c = 7\)

So the equation becomes \(x^2 + 18x + 77 = 0\) which gives x = -7 or -11.
So q must be -7.
\((-7)^2 - 7^2 = 0\)

Answer (D)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2683
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post 16 Sep 2014, 13:57
one way to solve it really fast is to factor it:
x=-11 thus we get (x+11)
in order to get x^2+18x+11c=0, q must be also a negative, otherwise we cannot get to this equation, therefore we get x+q

now we can factor (x+q)(x+11)=0
q+11=18
q*11=11c

since we need q^2-c^2, because every number squared to an even power is a positive number, 11q=11c=>q^2=c^2, and therefore q^2-c^2=0!
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1834
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post 22 Sep 2014, 02:44
LM wrote:
If q is one root of the equation x^2 + 18x + 11c = 0, where –11 is the other root and c is a constant, then q^2-c^2 =

A) 98
B) 72
C) 49
D) 0
E) It can't be determined from the information given


\(x^2 + 18x + 11c = 0\)

\(x^2 + (11 + 7)x + (11 * c) = 0\)

c = 7

Given one root = -11, so other root = -7 = q

\(c^2 - q^2 = 49 - 49 = 0\)

Answer = D
_________________

Kindly press "+1 Kudos" to appreciate :)

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 547
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post 05 May 2015, 13:51
We have roots q and -11, so using vieta's theorem X1*X2 = C --> q*(-11) = 11c -> q = -c then q^2 - c^2 = 0
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Intern
Intern
avatar
Joined: 13 Aug 2016
Posts: 2
Re: If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post 19 Feb 2017, 12:44
(x+11)(x+q) = 0

11+q = 18
q= 7
11*q = 77
11*c = 77
c=7
q^2 -c^2 =(-7)^2 - 7^2 = 0
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1087
Re: If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post 19 Feb 2017, 16:13
LM wrote:
If q is one root of the equation x^2 + 18x + 11c = 0, where –11 is the other root and c is a constant, then q^2-c^2 =

A) 98
B) 72
C) 49
D) 0
E) It can't be determined from the information given


if q and -11 are roots,
then (x-q)(x+11)=x^2-qx+11x-11q=0
-qx+11x=18x
q=-7
-11q=11c
c=7
(-7)^2-7^2=0
Manager
Manager
User avatar
S
Status: Preparing for GMAT!!
Joined: 11 Oct 2015
Posts: 135
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 660 Q47 V34
GMAT 2: 700 Q48 V38
GPA: 3.1
WE: General Management (Entertainment and Sports)
GMAT ToolKit User Premium Member
Re: If q is one root of the equation x^2 + 18x + 11c = 0, where  [#permalink]

Show Tags

New post 24 Feb 2017, 12:08
LM wrote:
If q is one root of the equation x^2 + 18x + 11c = 0, where –11 is the other root and c is a constant, then q^2-c^2 =

A) 98
B) 72
C) 49
D) 0
E) It can't be determined from the information given


Product of roots=c/a
=> \(q*-11=\frac{11c}{1}\)
=>\(c=-q\)

\(q^2-c^2=q^2-(-q)^2=q^2-q^2=0\)
_________________

Yours,
Siva Rama Krishna Meka :)

Re: If q is one root of the equation x^2 + 18x + 11c = 0, where &nbs [#permalink] 24 Feb 2017, 12:08
Display posts from previous: Sort by

If q is one root of the equation x^2 + 18x + 11c = 0, where

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

Events & Promotions

PREV
NEXT


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®.