Find all School-related info fast with the new School-Specific MBA Forum

It is currently 16 Apr 2014, 00:03

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

John and Jane started solving a quadratic equation. John mad

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Status: Still Struggling
Joined: 02 Nov 2010
Posts: 139
Location: India
GMAT Date: 10-15-2011
GPA: 3.71
WE: Information Technology (Computer Software)
Followers: 4

Kudos [?]: 6 [0], given: 8

John and Jane started solving a quadratic equation. John mad [#permalink] New post 20 Dec 2010, 07:20
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

90% (02:07) correct 9% (01:52) wrong based on 71 sessions
John and Jane started solving a quadratic equation. John made a mistake while copying the constant term and got the roots as 5 and 9. Jane made a mistake in the coefficient of x and she got the roots as 12 and 4.What is the equation?

A. x^2 + 4x + 14 = 0
B. 2x^2 + 7x -24 = 0
C. x^2 -14x + 48 = 0
D. 3x^2 -17x + 52 = 0
E. 2x^2 + 4x + 14 = 0
[Reveal] Spoiler: OA

_________________

Appreciation in KUDOS please!
Knewton Free Test 10/03 - 710 (49/37)
Princeton Free Test 10/08 - 610 (44/31)
Kaplan Test 1- 10/10 - 630
Veritas Prep- 10/11 - 630 (42/37)
MGMAT 1 - 10/12 - 680 (45/34)


Last edited by Bunuel on 09 Jul 2013, 09:02, edited 1 time in total.
Edited the question.
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17278
Followers: 2865

Kudos [?]: 18314 [1] , given: 2345

GMAT Tests User CAT Tests
Re: Problem in the roots [#permalink] New post 20 Dec 2010, 07:41
1
This post received
KUDOS
Expert's post
krishnasty wrote:
John and Jane started solving a quadratic equation. John made a mistake while copying the constant term and got the roots as 5 and 9. Jane made a mistake in the coefficient of x and she got the roots as 12 and 4.What is the equation?

a. x2 + 4x +14 =0
b. 2x2 +7x -24 =0
c. x2 -14x +48 =0
d. 3x2 -17x +52 =0
e. 2x2 + 4x +14 =0

Kindly explain..!!


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}.

John made a mistake while copying the constant term and got the roots as 5 and 9 so he copied coefficient of x and x^2 correctly: 5+9=14=-\frac{b}{a};

Jane made a mistake in the coefficient of x and she got the roots as 12 and 4 so she copied the constant term and the coefficient of x^2 correctly: 12*4=48=\frac{c}{a};

Only option C satisfies the above conditions x^2-14x+48=0: -\frac{b}{a}=-\frac{-14}{1}=14 and \frac{c}{a}=\frac{48}{1}=48 (any of the condition would be sufficient).

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Intern
Intern
Joined: 09 Nov 2010
Posts: 9
Followers: 0

Kudos [?]: 1 [0], given: 1

Re: Problem in the roots [#permalink] New post 21 Dec 2010, 03:56
Bunuel wrote:
krishnasty wrote:
John and Jane started solving a quadratic equation. John made a mistake while copying the constant term and got the roots as 5 and 9. Jane made a mistake in the coefficient of x and she got the roots as 12 and 4.What is the equation?

a. x2 + 4x +14 =0
b. 2x2 +7x -24 =0
c. x2 -14x +48 =0
d. 3x2 -17x +52 =0
e. 2x2 + 4x +14 =0

Kindly explain..!!


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}.

John made a mistake while copying the constant term and got the roots as 5 and 9 so he copied coefficient of x and x^2 correctly: 5+9=14=-\frac{b}{a};

Jane made a mistake in the coefficient of x and she got the roots as 12 and 4 so she copied the constant term and the coefficient of x^2 correctly: 12*4=48=\frac{c}{a};

Only option C satisfies the above conditions x^2-14x+48=0: -\frac{b}{a}=-\frac{-14}{1}=14 and \frac{c}{a}=\frac{48}{1}=48 (any of the condition would be sufficient).

Answer: C.



I just solve it with (x-y)(x-y) aproach not sure if I was just lucky and landed on the right answer or if it does always work :lol:

So: John got values 9 and 5 for x; (x-5)(x-9)=0 --> x^2-14x+45=0 (his mistake 45)
Jane got values 12 and 4 for x; (x-12)(x-4)=0 --> x^2-16x+48=0 (her mistake 16x)

Eliminate mistakes and plug in the right values each picked: X^2-14x(from Jonhs equ)+48(from janes)=0

Guess that this might only work when X^2 does not have a multiplier...

Will be adding to my "Blackbook" Viete's formula for the roots.
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4169
Location: Pune, India
Followers: 894

Kudos [?]: 3777 [0], given: 148

Re: Problem in the roots [#permalink] New post 21 Dec 2010, 12:43
Expert's post
itnas wrote:
John and Jane started solving a quadratic equation. John made a mistake while copying the constant term and got the roots as 5 and 9. Jane made a mistake in the coefficient of x and she got the roots as 12 and 4.What is the equation?

a. x2 + 4x +14 =0
b. 2x2 +7x -24 =0
c. x2 -14x +48 =0
d. 3x2 -17x +52 =0
e. 2x2 + 4x +14 =0

I just solve it with (x-y)(x-y) aproach not sure if I was just lucky and landed on the right answer or if it does always work :lol:

So: John got values 9 and 5 for x; (x-5)(x-9)=0 --> x^2-14x+45=0 (his mistake 45)
Jane got values 12 and 4 for x; (x-12)(x-4)=0 --> x^2-16x+48=0 (her mistake 16x)

Eliminate mistakes and plug in the right values each picked: X^2-14x(from Jonhs equ)+48(from janes)=0

Guess that this might only work when X^2 does not have a multiplier...

Will be adding to my "Blackbook" Viete's formula for the roots.


This approach isn't incorrect. It is perfectly fine and Viete's formula is good to know (I assume it is discussed in detail in high school in most curriculums).

It will work even if the equation has a co-efficient other than 1 for x^2. Lets say, rather than x2 -14x +48 =0, the given equation in options is: 2x^2 - 28x +96 =0. It doesn't matter since 2 is common to all terms and will be taken out and eliminated. So, in essence, the equation is still x2 -14x +48 =0.
Also if the equation is something like 4x^2 -28x + 45 =0, where nothing is common, the roots you obtain will reflect the co-efficient of x^2. i.e. roots of this equation are 5/2 and 9/2 and when you put it in the (x-a)(x-b) = 0 form, you get:
(x - 5/2)(x - 9/2) = 0
x^2 - 14/2 x + 45/4 = 0
4x^2 - 28x + 45 = 0

So according to the given roots, you will always get the accurate equation. It might have something common in all the terms but that equation will still be the same.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17278
Followers: 2865

Kudos [?]: 18314 [0], given: 2345

GMAT Tests User CAT Tests
Re: John and Jane started solving a quadratic equation. John mad [#permalink] New post 09 Jul 2013, 09:03
Expert's post
Re: John and Jane started solving a quadratic equation. John mad   [#permalink] 09 Jul 2013, 09:03
    Similar topics Author Replies Last post
Similar
Topics:
Popular new posts 2 In The Dynamics of Apocalypse, John Lowe attempts to solve HIMALAYA 19 30 May 2005, 22:07
New posts 3 John can complete a given task in 20 days. Jane will take arjtryarjtry 7 20 Jul 2008, 04:23
Popular new posts 1 Experts publish their posts in the topic Jane and John are very concerned about their five-year-old smodak 12 19 May 2011, 05:09
New posts solving quadratic equations pro 3 08 Jun 2011, 14:15
New posts John encouraged Jerry to start a pest control business TGC 3 05 May 2013, 03:48
Display posts from previous: Sort by

John and Jane started solving a quadratic equation. John mad

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.