It is currently 13 Dec 2017, 20:40

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M18-35

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

M18-35 [#permalink]

Show Tags

New post 16 Sep 2014, 00:04
Expert's post
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:04) correct 43% (01:10) wrong based on 145 sessions

HideShow timer Statistics

If set \(M\) consists of the root(s) of equation \(2-x^2 = (x-2)^2\), what is the range of set \(M\)?

A. 0
B. \(\frac{1}{\sqrt{2}}\)
C. 1
D. \(\sqrt{2}\)
E. 2
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 135562 [0], given: 12699

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [1], given: 12699

Re M18-35 [#permalink]

Show Tags

New post 16 Sep 2014, 00:05
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Official Solution:

If set \(M\) consists of the root(s) of equation \(2-x^2 = (x-2)^2\), what is the range of set \(M\)?

A. 0
B. \(\frac{1}{\sqrt{2}}\)
C. 1
D. \(\sqrt{2}\)
E. 2


\(2-x^2 = (x-2)^2\);

\(2-x^2=x^2-4x+4\);

\(x^2-2x+1=0\);

\((x-1)^2=0\);

\(x=1\). So, set \(M\) consists of only one element.

The range of a single element set is 0.


Answer: A
_________________

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

Kudos [?]: 135562 [1], given: 12699

Intern
Intern
avatar
B
Joined: 15 Oct 2013
Posts: 9

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

Concentration: Accounting
GPA: 3.01
WE: Accounting (Accounting)
Re: M18-35 [#permalink]

Show Tags

New post 25 May 2015, 13:43
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

Re: M18-35 [#permalink]

Show Tags

New post 26 May 2015, 05:32
whitdiva23 wrote:
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.


\(2 - x^ 2 = x^2 - 4x + 4\);

Re-arrange: \(2x^2 - 4x +2 = 0\);

Reduce by 2: \(x^2 -2x + 1 = 0\), which is the same as \((x−1)^2=0\), so \(x=1\).
_________________

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

Kudos [?]: 135562 [0], given: 12699

Intern
Intern
avatar
B
Joined: 15 Jan 2014
Posts: 22

Kudos [?]: 17 [0], given: 26

Location: India
Concentration: Technology, Strategy
Schools: Haas '19
GMAT 1: 650 Q49 V30
GPA: 2.5
WE: Information Technology (Consulting)
Re: M18-35 [#permalink]

Show Tags

New post 10 Feb 2017, 08:47
Hi Bunuel

I think

\((x−1)^2\)=0 will give 2 equal values for X(1,1) not single value . So range will be 0.

Is this correct ?

Thanks

Kudos [?]: 17 [0], given: 26

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

Re: M18-35 [#permalink]

Show Tags

New post 10 Feb 2017, 09:00

Kudos [?]: 135562 [0], given: 12699

Intern
Intern
avatar
B
Joined: 03 May 2014
Posts: 14

Kudos [?]: [0], given: 3

CAT Tests
Re: M18-35 [#permalink]

Show Tags

New post 16 Nov 2017, 07:56
Bunuel wrote:
whitdiva23 wrote:
Is there anyway that someone can show me how they got the answer of 0? I can get this far:

2-x^2 = (X-2)^2

2-X^2 = (X-2) (X-2)

2-X^ 2 = X^2-4X+4

What to do after this. I don't understand the break down on the free GMAT text. It's not clicking at this moment.


\(2 - x^ 2 = x^2 - 4x + 4\);

Re-arrange: \(2x^2 - 4x +2 = 0\);

Reduce by 2: \(x^2 -2x + 1 = 0\), which is the same as \((x−1)^2=0\), so \(x=1\).


How would one know when to reduce the equation as opposed to trying to solve a quadratic equation ax^2 +bx + c when a>1. For example factoring out the 2x^2?

Kudos [?]: [0], given: 3

Re: M18-35   [#permalink] 16 Nov 2017, 07:56
Display posts from previous: Sort by

M18-35

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

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.