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

It is currently 01 Aug 2015, 00:38
GMAT Club Tests

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

Another fresh question on 2 Part- Quadratic function

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
Joined: 02 Nov 2011
Posts: 1868
Followers: 1591

Kudos [?]: 4783 [1] , given: 219

Another fresh question on 2 Part- Quadratic function [#permalink] New post 25 Jan 2013, 03:56
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Try yet another 2 part question- fresh from the e-GMAT bakery!

A function f(x, y) is such that \(f(x,y)=3x^2-2xy+y^2+4\). Select one value for x, & one value for y such that given information implies that f(x, y) = 8. Make only two selections, one in each column.

Image

This is a representative question of OG13/# 38. Want to view similar 2 part questions with an interactive audio visual solution? Register here at e-GMAT.

-Shalabh

Last edited by egmat on 02 Feb 2013, 22:46, edited 1 time in total.
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
4 KUDOS received
Current Student
User avatar
Joined: 27 Jun 2012
Posts: 418
Concentration: Strategy, Finance
Followers: 58

Kudos [?]: 482 [4] , given: 182

Re: Another fresh question on 2 Part- Quadratic function [#permalink] New post 25 Jan 2013, 16:23
4
This post received
KUDOS
Answer: \(x = 1\) and \(y= 1-\sqrt{2}\)

I used back-solving method to solve this problem by substituting values for x in following order \((0, 1, -1, 1-\sqrt{2})\)

Given that,
\(f(x,y)=3x^2-2xy+y^2+4=8\)
i.e. \(3x^2-2xy+y^2=4\) -- To be proved

Substituting \(x=0\) gives \(y=\pm2\) which is not in the answer list.

Substitute \(x=1\)
\(3x^2-2xy+y^2=4\)
\(3*1^2-2(1)y+y^2=4\)
\(3-2y+y^2=4\)
\(y^2-2y-1=0\)

As we know \(x = [-b\pm\sqrt{b^2-4ac}]/2a\) are roots for \(ax^2+bx+c=0\)

\(y= [-(-2)\pm\sqrt{(-2)^2-4(1)(-1)}]/2(1)=[2\pm\sqrt{(8)}]/2=1-\sqrt{2}\)


Hence Answer: \(x = 1\) and \(y= 1-\sqrt{2}\)
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
Reading Comprehension notes: Click here
VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

Director
Director
avatar
Joined: 08 Jun 2010
Posts: 680
Followers: 0

Kudos [?]: 47 [0], given: 152

Re: Another fresh question on 2 Part- Quadratic function [#permalink] New post 28 Jan 2013, 23:14
how to pick the number ? picking number is time consuming.

any tip, trick here,
Expert Post
e-GMAT Representative
User avatar
Joined: 02 Nov 2011
Posts: 1868
Followers: 1591

Kudos [?]: 4783 [0], given: 219

Re: Another fresh question on 2 Part- Quadratic function [#permalink] New post 01 Feb 2013, 01:48
Expert's post
thangvietnam wrote:
how to pick the number ? picking number is time consuming.

any tip, trick here,

Hi,

When we look at \(f(x,y)=3x^2-2xy+y^2+4\) and then at the options, we find that plugging values is the best way to approach this question.
There are 3 things that should be keptp in mind while picking option values.

1.Pick integers first. They are easy to work on.
There are 3 values in the option list, which are integers.

2.Pick ‘0’ first. This will eliminate one variable completely for compuation.

3.What to choose first; x or y? One should always observe right hand side of the function. If number of terms of x is more than the number of terms of y, then plug in the option value in x first, and vice versa.


We choose the values for x in the order of 0, 1, and -1 to plug in.

Now, we plug in the value of f(x, y) =8, & x=0 in the equation, and we get,

\(8=3.0^2-2.0.y+y^2+4\)
\(8=y^2+4\)
\(4=y^2\)
y= ±2

This means for x=0, y is either 2 or -2. There is no such option available for values: 2 or-2 , hence these pair of values cannot be correct.

Now, we should try x=1. You may follow PraPon’s solution for x=1. He has done it correctly.

Hope it helps!

-Shalabh
_________________

Aiming to score 760+ on the GMAT? Attend our free webinars to learn how to:

[*] Master Number Properties
[*] Ace Critical Reasoning

The webinars will start at 7 AM PST on the 11th and 12th of July, 2015.

Intern
Intern
avatar
Joined: 19 May 2012
Posts: 36
Location: India
Concentration: International Business, Healthcare
GMAT Date: 03-03-2014
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 7 [0], given: 0

Re: Another fresh question on 2 Part- Quadratic function [#permalink] New post 02 Mar 2013, 07:09
x=1,
y=1-root(2)
_________________

Thanks
crazy4priya
GMATPrep 1 710/Q49/V38
GMATPrep 2 690/Q49/V34
Veritas Prep 700/Q50/V36/IR5
MGMT Test 1 700/Q51/V35/IR3

Intern
Intern
User avatar
Joined: 11 May 2013
Posts: 1
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: Another fresh question on 2 Part- Quadratic function [#permalink] New post 10 Nov 2013, 12:15
\(f(x,y) = 3x^2 - 2xy + y^2 + 4 = 2x^2 + (x-y)^2 + 4\)
So, \(f(x,y) = 8\) if and only if \(2x^2 + (x-y)^2 = 4\) or \(x^2 + ((x-y)/sqrt 2)^2 = 2\)

Now that you have formulated the expression this way, it is very easy to see that x=1 and y=1-sqrt(2) is the solution.

This is much faster than plugging in values.
Re: Another fresh question on 2 Part- Quadratic function   [#permalink] 10 Nov 2013, 12:15
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic A 2 Part question egmat 5 01 Jan 2013, 21:48
4 Experts publish their posts in the topic A tricky 2 Part Question on Multi Level Marketing (MLM) egmat 15 18 Dec 2012, 05:47
1 Experts publish their posts in the topic 2-Part IR Question egmat 3 03 Dec 2012, 09:39
2 2 Part question- Max., & Min. value of function! ShalabhsQuants 9 09 Sep 2012, 06:39
2 2 Part question! ShalabhsQuants 2 07 Sep 2012, 06:00
Display posts from previous: Sort by

Another fresh question on 2 Part- Quadratic function

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.