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

It is currently 23 Oct 2018, 22:08

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

Another fresh question on 2 Part- Quadratic function

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

Hide Tags

e-GMAT Representative
User avatar
G
Joined: 02 Nov 2011
Posts: 2711
Another fresh question on 2 Part- Quadratic function  [#permalink]

Show Tags

New post Updated on: 02 Feb 2013, 23:46
1
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

Originally posted by egmat on 25 Jan 2013, 04:56.
Last edited by egmat on 02 Feb 2013, 23:46, edited 1 time in total.
Senior Manager
Senior Manager
User avatar
Joined: 27 Jun 2012
Posts: 377
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: Another fresh question on 2 Part- Quadratic function  [#permalink]

Show Tags

New post 25 Jan 2013, 17:23
5
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 GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here
Finance your Student loan through SoFi and get $100 referral bonus : Click here

Director
Director
avatar
S
Joined: 09 Jun 2010
Posts: 937
Re: Another fresh question on 2 Part- Quadratic function  [#permalink]

Show Tags

New post 29 Jan 2013, 00:14
how to pick the number ? picking number is time consuming.

any tip, trick here,
e-GMAT Representative
User avatar
G
Joined: 02 Nov 2011
Posts: 2711
Re: Another fresh question on 2 Part- Quadratic function  [#permalink]

Show Tags

New post 01 Feb 2013, 02:48
2
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
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
Joined: 19 May 2012
Posts: 30
Location: India
Concentration: International Business, Healthcare
GMAT Date: 03-03-2014
WE: Information Technology (Computer Software)
Re: Another fresh question on 2 Part- Quadratic function  [#permalink]

Show Tags

New post 02 Mar 2013, 08:09
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
Re: Another fresh question on 2 Part- Quadratic function  [#permalink]

Show Tags

New post 10 Nov 2013, 13:15
\(f(x,y) = 3x^2 - 2xy + y^2 + 4 = 2x^2 + (x-y)^2 + 4\)
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.
Intern
Intern
avatar
B
Joined: 22 Jun 2017
Posts: 16
Location: India
GMAT 1: 670 Q48 V34
GPA: 4
Re: Another fresh question on 2 Part- Quadratic function  [#permalink]

Show Tags

New post 25 Nov 2017, 06:32
Here is another trick as number picking can be a longer process !
Solve and separate out for quadratic
we know we have to prove 3x^2-2xy+y^2=4
i will simplify this as 2x^2+(x-y)^2=4 ...... from here choosing x =1 and y = 1-root2 becomes easy

Kudos if it helps
GMAT Club Bot
Re: Another fresh question on 2 Part- Quadratic function &nbs [#permalink] 25 Nov 2017, 06:32
Display posts from previous: Sort by

Another fresh question on 2 Part- Quadratic function

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

Moderators: chetan2u, Bunuel



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®.