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

It is currently 17 Aug 2018, 02:53

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

Which of the following equation has 3+2[m][square_root] 3 [/square_roo

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

Hide Tags

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 1897
Which of the following equation has 3+2[m][square_root] 3 [/square_roo  [#permalink]

Show Tags

New post 30 Jun 2018, 11:10
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (01:32) correct 41% (01:39) wrong based on 91 sessions

HideShow timer Statistics

Question-2



Which of the following equation has \(3+2\sqrt{3}\) as one of its roots?

Options


A. \(x^2+6x+3 = 0\)
B. \(x^2-6x+3 = 0\)
C. \(x^2+6x-3 = 0\)
D. \(x^2-6x-3 = 0\)
E. \(x^2-4 \sqrt{3}x-3 = 0\)

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



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

Senior Manager
Senior Manager
User avatar
G
Joined: 29 Dec 2017
Posts: 338
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GPA: 3.25
WE: Marketing (Telecommunications)
Which of the following equation has 3+2[m][square_root] 3 [/square_roo  [#permalink]

Show Tags

New post Updated on: 01 Jul 2018, 06:25
One of the ways is to approximate the value of \(3+2\sqrt{3}\) =3+2*1.7=6.4
Substitute 6.4 for x

Only option D. \(x^2-6x-3 = 0\) will work with the value. Answer D.
_________________

I'm looking for a study buddy in NY, who is aiming at 700+. PM me.


Originally posted by Hero8888 on 30 Jun 2018, 15:04.
Last edited by Hero8888 on 01 Jul 2018, 06:25, edited 2 times in total.
Manager
Manager
User avatar
B
Joined: 07 Feb 2017
Posts: 167
Re: Which of the following equation has 3+2[m][square_root] 3 [/square_roo  [#permalink]

Show Tags

New post 30 Jun 2018, 16:14
1
(X-(3+2sqrt(3))(x-(3-2sqrt(3))
=x^2-(3-2sqrt(3))x-(3+2sqrt(3))x-3
=x^2-6x-3
Answer D

Posted from my mobile device
Intern
Intern
User avatar
B
Joined: 09 Jun 2018
Posts: 25
Location: United States (IN)
GPA: 3.95
WE: Engineering (Transportation)
GMAT ToolKit User
Re: Which of the following equation has 3+2[m][square_root] 3 [/square_roo  [#permalink]

Show Tags

New post 30 Jun 2018, 19:54
1
Here's my solution: If one root is 3+2\(\sqrt{3}\), then other root is 3-2\(\sqrt{3}\).

Sum of roots = 6
Product of roots = 9-(4*3) = -3

Hence equation is: \(x^{2}\) - (sum of roots)*x + (product of roots) = \(x^{2}\)- 6x -3

Hence D
_________________

If you found this relevant and useful, please Smash that Kudos button!

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 1897
Re: Which of the following equation has 3+2[m][square_root] 3 [/square_roo  [#permalink]

Show Tags

New post 04 Jul 2018, 03:45

Solution



Given:
    • One of the roots of a quadratic equation is \(3 + 2\sqrt{3}\)

To find:
    • The original equation, with the given root \(3 + 2\sqrt{3}\)

Approach and Working:
We know that if one of the roots of a quadratic equation is \(a + \sqrt{b}\), then as a conjugate root, the other one will be \(a – \sqrt{b}\)

Therefore, the roots of the given equation will be:
    • \(3 + 2\sqrt{3}\)
    • \(3 – 2\sqrt{3}\)

So, the equation can be:
    • \([x – (3 + 2\sqrt{3})] [x – (3 – 2\sqrt{3})] = 0\)
    Or, \((x – 3 – 2\sqrt{3}) (x – 3 + 2\sqrt{3}) = 0\)
    Or, \(x^2 – 3x + 2\sqrt{3}x – 3x + 9 – 6\sqrt{3} – 2\sqrt{3}x + 6\sqrt{3} – 12 = 0\)
    Or, \(x^2 – 6x – 3 = 0\)

Hence, the correct answer is option D.

Answer: D
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



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

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 1897
Which of the following equation has 3+2[m][square_root] 3 [/square_roo  [#permalink]

Show Tags

New post 04 Jul 2018, 03:57

Alternate Solution



Given:
    • One of the roots of a quadratic equation is \(3 + 2\sqrt{3}\)

To find:
    • The original equation, with the given root \(3 + 2\sqrt{3}\)

Approach and Working:
    • The value of \((3 + 2\sqrt{3})^2 = 9 + 12 + 12\sqrt{3} = 21 + 12\sqrt{3}\)

Replacing the value of \(x^2\) and \(x\) in the given options, we get:
    • \(21 + 12\sqrt{3} + 18 + 12\sqrt{3} + 3\)
      o Not equal to 0

    • \(21 + 12\sqrt{3} – 18 – 12\sqrt{3} + 3\)
      o Not equal to 0

    • \(21 + 12\sqrt{3} + 18 + 12\sqrt{3} – 3\)
      o Not equal to 0

    • \(21 + 12\sqrt{3} – 18 – 12\sqrt{3} – 3\)
      o Equal to 0

    • \(21 + 12\sqrt{3} – 24 – 12\sqrt{3} – 3\)
      o Not equal to 0

Hence, the correct answer is option D.

Answer: D
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



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

Intern
Intern
avatar
B
Joined: 17 Jun 2018
Posts: 8
Re: Which of the following equation has 3+2[m][square_root] 3 [/square_roo  [#permalink]

Show Tags

New post 04 Jul 2018, 20:25
We are given that one of the root is 3+2√3, so another root is 3-2√3.
(We know that if one of the roots of a quadratic equation is a+√b, then as a conjugate root, the other one will be a–√b)
All the quadratic equation can be expressed as aX^2+bX+C=y
Let the two different roots be X1 and X2
X1=3+2√3
X2=3-2√3
X1 * X2 =-3
X1+X2 = 6

We also know that:
X1*X2 = c/a
X1+X2 = -b/a

A. x^2+6x+3=0
X1*X2 = 3
X1+X2 = -6
Not the answer we are looking for.
B. x^2−6x+3=0
X1*X2 = 3
X1+X2 = 6
Not the answer we are looking for.
C. x^2+6x−3=0
X1*X2 = -3
X1+X2 = -6
Not the answer we are looking for.
D. x^2−6x−3=0
X1*X2 = -3
X1+X2 = 6
Bingo, this is the answer choice we are looking for.
E. x^2−43√x−3=0
Re: Which of the following equation has 3+2[m][square_root] 3 [/square_roo &nbs [#permalink] 04 Jul 2018, 20:25
Display posts from previous: Sort by

Which of the following equation has 3+2[m][square_root] 3 [/square_roo

  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®.