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

It is currently 20 Oct 2018, 14:24

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 f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value

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

Hide Tags

Director
Director
User avatar
Joined: 25 Oct 2008
Posts: 516
Location: Kolkata,India
If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post Updated on: 04 Mar 2018, 07:33
2
14
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (02:35) correct 42% (03:08) wrong based on 103 sessions

HideShow timer Statistics

If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all values for k such that f(k + 2) = g(2k)?

A. -8
B. -4
C. 4
D. 8
E. 65


Looks pretty simple..however I got stuck mid-way.
Got till \(K^2-4K-65=0\)
Does anyone know how to proceed further??

_________________

http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902


Originally posted by tejal777 on 29 Oct 2009, 02:38.
Last edited by Bunuel on 04 Mar 2018, 07:33, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 29 Oct 2009, 03:28
17
7
tejal777 wrote:
If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all values for k such that f(k + 2) = g(2k)?

A. -8
B. -4
C. 4
D. 8
E. 65

Looks pretty simple..however I got stuck mid-way.
Got till \(K^2-4K-65=0\)
Does anyone know how to proceed further??


You've done everything right:

\(5*(k+2)^2=(2k)^2+12(2k)+85\) --> \(k^2-4k-65=0\).

Viete's formula for the roots \(x_1\) and \(x_2\) of equation \(ax^2+bx+c=0\):

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

So in our case the roots \(k_1+k_2=\frac{-(-4)}{1}=4\)

Answer: C.
_________________

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
Senior Manager
Senior Manager
User avatar
Joined: 18 Aug 2009
Posts: 284
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 29 Oct 2009, 03:39
1
Bunuel wrote:
tejal777 wrote:
\(If f(x)=5x^2 and g(x)=x^2 + 12x + 85\), what is the sum of all values for k such that f (k+2)=g(2k) ?

Looks pretty simple..however I got stuck mid-way.
Got till \(K^2-4K-65=0\)
Does anyone know how to proceed further??


You've done everything right:

\(5*(k+2)^2=(2k)^2+12(2k)+85\) --> \(k^2-4k-65=0\).

Viete's formula for the roots \(x1\) and \(x2\) of equation \(ax^2+bx+c=0\):

\(x1+x2=\frac{-b}{a}\) AND \(x1*x2=\frac{c}{a}\)

So in our case the roots \(k1+k2=\frac{-(-4)}{1}=4\)



Wow! math buster :)
don't have it in GMAT notes... added now, thnx and +1
Manager
Manager
avatar
Joined: 15 Sep 2009
Posts: 117
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 29 Oct 2009, 04:36
after simplification,we get the quadratic eqn

k^2-4k-65= 0

sum of all values of k will be equal to the sum of the roots of the above q.eqn = -b/a = 4

I will go with 4
Intern
Intern
avatar
Affiliations: CA - India
Joined: 27 Oct 2009
Posts: 43
Location: India
Schools: ISB - Hyderabad, NSU - Singapore
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 29 Oct 2009, 05:47
I tried solving this by quadratic equation formula and got 2 answers - 2+ or -\sqrt{65}.

What could be the other two possible values of k?
Retired Moderator
avatar
B
Joined: 16 Nov 2010
Posts: 1436
Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 09 May 2011, 05:40
1
5(k+2)^2 = 4k^2 + 24k + 85

=> 5(k^2 + 4k + 4) = 4k^2 + 24k + 85

=> 5k^2 + 20k + 20 = 4k^2 + 24k + 85

=> k^2 - 4k - 65 = 0

No need to solve this, we need sum of two values of k:

So sum of roots = -b/a = -(-4) = 4
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

VP
VP
User avatar
Status: Current Student
Joined: 24 Aug 2010
Posts: 1338
Location: United States
GMAT 1: 710 Q48 V40
WE: Sales (Consumer Products)
Premium Member Reviews Badge
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 09 May 2011, 14:39
f(x)=5x^2
g(x)=x^2+12x+85
f(k+2)=5 (k+2)^2= 5(k^2+4k+4)=5k^2+20k+20

g(2k)= (2k)^2+ 12(2k)+85=4k^2+24k+85

5^k2+20k+20=4k^2+24k+85
k^2-4k-65=0

Using the quadratic equation (-b +/-\sqrt{b2-4ac}/2a we find the roots as follows

-(-4)+/-\sqrt{4^2 - 4(1)(-65)}/2(1)
So the first root is
4+\sqrt{16+260}/2 = 4+\sqrt{276}/2= 4+2\sqrt{69}/2
The second root is
4-\sqrt{16+260}/2 = 4-\sqrt{276}/2= 4-2\sqrt{69}/2

The sum of the roots is
4+2\sqrt{69}/2 + 4-2\sqrt{69}/2 = 8/2= 4
The answer should be 4 :-D
_________________

The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 668
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 09 May 2011, 16:59
sum of two roots of a quadratic equation is -b/a


now we have \(k^2-4k-65\)

=> - b/a = 4
Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 341
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 07 Oct 2012, 01:38
How do we get 4??

-b/a?? what is concept behind it??

k2-4k-65=0?? i cant solve after that..

plz do explain..Thanks in advance
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 07 Oct 2012, 04:48
1
2
sanjoo wrote:
How do we get 4??

-b/a?? what is concept behind it??

k2-4k-65=0?? i cant solve after that..

plz do explain..Thanks in advance


It's called Viete's theorem, which 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 \(x_1*x_2=\frac{c}{a}\).

Now, if we apply this to \(k^2-4k-65=0\), we'll get that the sum of the roots must be \(k_1+k_2=\frac{-(-4)}{1}=4\).

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

Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 341
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 07 Oct 2012, 10:59
Thanks Alot BUNUEL..

i didnt see formula like this in my life :( new things very hard to digest :(..
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 431
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 10 Dec 2012, 05:13
\(f(k+2) = 5(k+2)^2 = 5(k^2 + 4k + 4) = 5k^2 + 20k + 20\)
\(g(2k) = 4k^2 + 24k + 85\)

\(5k^2 + 20k + 20 = 4k^2 + 24k + 85\)
\(k^2 - 4k -65 = 0\)

Trick: Sum of all roots: k1 + k2 = -b/a

\(k1 + k2 = - \frac{-4}{1} = 4\)

Answer: 4
_________________

Impossible is nothing to God.

Manager
Manager
User avatar
B
Joined: 26 Feb 2018
Posts: 59
WE: Sales (Internet and New Media)
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 04 Mar 2018, 07:25
Bunuel ,

Can we have more this kinda questions of functions ?
_________________

" Can't stop learning and failing"

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 04 Mar 2018, 07:35
1
loserunderachiever wrote:
Bunuel ,

Can we have more this kinda questions of functions ?


13. Functions



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________

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

Manager
Manager
User avatar
B
Joined: 26 Feb 2018
Posts: 59
WE: Sales (Internet and New Media)
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value  [#permalink]

Show Tags

New post 04 Mar 2018, 07:46
Thanks a lot Bunuel !
_________________

" Can't stop learning and failing"

GMAT Club Bot
Re: If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value &nbs [#permalink] 04 Mar 2018, 07:46
Display posts from previous: Sort by

If f(x) = 5x^2 and g(x) = x^2 + 12x + 85, what is the sum of all value

  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®.