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

It is currently 24 Oct 2014, 09:26

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

Which of the following describes all values of x for which

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 27 Mar 2008
Posts: 81
Followers: 1

Kudos [?]: 14 [0], given: 0

Which of the following describes all values of x for which [#permalink] New post 16 Aug 2008, 10:58
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

74% (01:38) correct 26% (00:40) wrong based on 156 sessions
Which of the following describes all values of x for which 1-x^2 ≥ 0 ?

A. x ≥ 1
B. x ≤ -1
C. 0 ≤ x ≤ 1
D. x ≤ -1 or x ≥ 1
E. -1 ≤ x ≤ 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Apr 2012, 02:41, edited 2 times in total.
Edited the question and added the OA
SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1829
Location: New York
Followers: 27

Kudos [?]: 472 [0], given: 5

Re: PS: Inequality [#permalink] New post 16 Aug 2008, 13:49
droopy57 wrote:
Which of the following describes all values of x for which 1-x^2 >= 0 ?

(a) x ≥ 1
(b) x ≤ -1
(c) 0 ≤ x ≤ 1
(d) x ≤ -1 or x ≥ 1
(e) -1 ≤ x ≤ 1

Please expand on answers


E.

1-x^2 >= 0 ---> x^2-1<=0
--> (x+1)(x-1)<=0
Above equation true for
i) x+1<=0 and x-1>=0 ---> x<= -1 and x>=1 ---> this is not possible ---Strike out this solution
ii) x+1>=0 and x-1<=0 ---> x>=-1 and x<=1 --> -1<=x<=1
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Manager
Manager
avatar
Joined: 30 May 2008
Posts: 76
Followers: 0

Kudos [?]: 14 [0], given: 26

Re: PS: Inequality [#permalink] New post 20 Apr 2012, 01:18
x2suresh wrote:
droopy57 wrote:
Which of the following describes all values of x for which 1-x^2 >= 0 ?

(a) x ≥ 1
(b) x ≤ -1
(c) 0 ≤ x ≤ 1
(d) x ≤ -1 or x ≥ 1
(e) -1 ≤ x ≤ 1

Please expand on answers


E.

1-x^2 >= 0 ---> x^2-1<=0
--> (x+1)(x-1)<=0
Above equation true for
i) x+1<=0 and x-1>=0 ---> x<= -1 and x>=1 ---> this is not possible ---Strike out this solution
ii) x+1>=0 and x-1<=0 ---> x>=-1 and x<=1 --> -1<=x<=1


Can someone please explain the signs in red above? this is not absolute value, why do we need to test these?
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28902 [3] , given: 2871

Re: PS: Inequality [#permalink] New post 20 Apr 2012, 03:08
3
This post received
KUDOS
Expert's post
catty2004 wrote:
x2suresh wrote:
droopy57 wrote:
Which of the following describes all values of x for which 1-x^2 >= 0 ?

(a) x ≥ 1
(b) x ≤ -1
(c) 0 ≤ x ≤ 1
(d) x ≤ -1 or x ≥ 1
(e) -1 ≤ x ≤ 1

Please expand on answers


E.

1-x^2 >= 0 ---> x^2-1<=0
--> (x+1)(x-1)<=0
Above equation true for
i) x+1<=0 and x-1>=0 ---> x<= -1 and x>=1 ---> this is not possible ---Strike out this solution
ii) x+1>=0 and x-1<=0 ---> x>=-1 and x<=1 --> -1<=x<=1


Can someone please explain the signs in red above? this is not absolute value, why do we need to test these?


Actually you can transform it to an absolute value problem: 1-x^2\geq{0} --> x^2\leq{1}, since both parts of the inequality are non-negative then we can take square root: |x|\leq{1} --> -1\leq{x}\leq{1}.

Now, other approach would be: 1-x^2\geq{0} --> x^2-1\leq{0} --> (x+1)(x-1)\leq{0} --> the roots are -1 and 1 --> "<" sign indicates that the solution lies between the roots, so -1\leq{x}\leq{1}.


Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Now, about x2suresh's approach: we have (x+1)(x-1)\leq{0}, so the product of two multiples is less than (or equal to) zero, which means that the multiples must have opposite signs. Then x2suresh checks the case A. when the first multiple (x+1) is negative and the second (x-1) is positive and the case B. when the first multiple (x+1) is positive and the second (x-1) is negative to get the range for which (x+1)(x-1)\leq{0} holds true. Notice that, for this particular problem, we don't realy need to test case A, since it's not possible (x+1), the larger number, to be negative and (x-1), the smaller number to be positive. As for case B, it gives: x+1\geq{0} and x-1\leq{0} --> x1\geq{-1} and x\leq{1} --> -1\leq{x}\leq{1}.

Hope it helps.
_________________

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 30 May 2008
Posts: 76
Followers: 0

Kudos [?]: 14 [0], given: 26

Re: PS: Inequality [#permalink] New post 20 Apr 2012, 08:55
Thank you soooooooooooo much Bunuel!!

Bunuel wrote:
catty2004 wrote:
Can someone please explain the signs in red above? this is not absolute value, why do we need to test these?


Actually you can transform it to an absolute value problem: 1-x^2\geq{0} --> x^2\leq{1}, since both parts of the inequality are non-negative then we can take square root: |x|\leq{1} --> -1\leq{x}\leq{1}.

Now, other approach would be: 1-x^2\geq{0} --> x^2-1\leq{0} --> (x+1)(x-1)\leq{0} --> the roots are -1 and 1 --> "<" sign indicates that the solution lies between the roots, so -1\leq{x}\leq{1}.


Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535
everything-is-less-than-zero-108884.html?hilit=extreme#p868863

Now, about x2suresh's approach: we have (x+1)(x-1)\leq{0}, so the product of two multiples is less than (or equal to) zero, which means that the multiples must have opposite signs. Then x2suresh checks the case A. when the first multiple (x+1) is negative and the second (x-1) is positive and the case B. when the first multiple (x+1) is positive and the second (x-1) is negative to get the range for which (x+1)(x-1)\leq{0} holds true. Notice that, for this particular problem, we don't realy need to test case A, since it's not possible (x+1), the larger number, to be negative and (x-1), the smaller number to be positive. As for case B, it gives: x+1\geq{0} and x-1\leq{0} --> x1\geq{-1} and x\leq{1} --> -1\leq{x}\leq{1}.

Hope it helps.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28902 [0], given: 2871

Re: Which of the following describes all values of x for which [#permalink] New post 17 Jun 2013, 04:51
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


_________________

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

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Which of the following describes all values of x for which   [#permalink] 17 Jun 2013, 04:51
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Which of the following describes all the values of x for whi goodyear2013 3 30 Jul 2014, 01:53
14 Experts publish their posts in the topic Which of the following describes all the values of y for whi vabhs192003 18 14 Oct 2013, 09:15
1 Experts publish their posts in the topic Which of the following describes all values of n for which n hb 1 26 Jul 2013, 14:58
6 Experts publish their posts in the topic Which of the following describes all values of x for which 1 Walkabout 5 20 Dec 2012, 08:15
Which of the following describes all values of x for which 1 above720 2 23 Aug 2007, 17:18
Display posts from previous: Sort by

Which of the following describes all values of x for which

  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®.