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

It is currently 15 Dec 2018, 13:28

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

Which of the following describes all values of x for which 1

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

Hide Tags

Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 177
Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 20 Dec 2012, 08:15
4
12
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (01:12) correct 27% (01:23) wrong based on 895 sessions

HideShow timer Statistics

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
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 20 Dec 2012, 08:16
4
2
Most Helpful Community Reply
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 684
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 27 May 2014, 02:37
5
1
jatinsachani wrote:
Bunuel wrote:
Walkabout 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


\(1-x^2\geq{0}\) --> \(x^2\leq{1}\) --> \(-1\leq{x}\leq{1}\).

Answer: E.



Bunuel, Can you explain how we go from \(x^2\) to x in last step


Hello,

You have \(1-x^2\geq{0}\).
Since LHS and RHS are non-negative,we can take square root on both sides and get

\(1\geq{\sqrt{x^2}}\)

Also, \(\sqrt{x^2}\)=|x| so we have \(|x|\leq{1}\)
So x is between \(-1\leq{x}\leq{1}\)

Also, you can do it as \(1-x^2\geq{0}\) or \((1-x)(1+x)\geq{0}\) (using \(a^2-b^2=(a-b)(a+b)\) )

We need to find in which region does the equation hold true...try values of x <-1, -1<x<1 and x>1 to see where the relationship holds true

You need to brush your basics on mod values. Check out below links

graphic-approach-to-problems-with-inequalities-68037.html
math-number-theory-88376.html
if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

General Discussion
Intern
Intern
User avatar
Joined: 24 Aug 2013
Posts: 5
Re: Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 27 May 2014, 01:57
Bunuel wrote:
Walkabout 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


\(1-x^2\geq{0}\) --> \(x^2\leq{1}\) --> \(-1\leq{x}\leq{1}\).

Answer: E.



Bunuel, Can you explain how we go from \(x^2\) to x in last step
Intern
Intern
avatar
Joined: 29 Jan 2014
Posts: 4
Re: Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 27 May 2014, 02:17
Which of the following describes all values of x for which 1–x^2 >= 0?

(A) x >= 1

Plugged in 2. 1–(2)^2 >= 0 -3>=0? NO. Wrong

(B) x <= –1

Plugged in -2. 1–(-2)^2 >= 0 -3>=0? NO. Wrong

(C) 0 <= x <= 1
Plugged in 0, 1, and 1/2. All of them work. But E is better because it describes all the values of x

(D) x <= –1 or x >= 1
A and B answer this. Wrong.

(E) –1 <= x <= 1

X is a positive or negative fraction or a zero.
x = -1/2 x = 1/2 x = 0
Plug all of them. They work.
Answer is E.

Another solution:
1–x^2 >= 0
1>= x^2
Therefore, -1=<x=<1
Intern
Intern
avatar
Joined: 08 Jan 2014
Posts: 1
Premium Member
Re: Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 26 Jun 2014, 15:16
2
(1-x^2) >= 0 can be expressed as (1-x) (1+x) >=0

So 1-x>=0 (OR) 1+x>=0.

Therefore, 1 >= x (OR) x >= -1
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13087
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 30 Sep 2015, 10:13
1
Hi All,

With inequality-based questions, sometimes the easiest approach is just to come up with a few examples that 'fit' the given prompt and then use those examples to eliminate answer choices.

Here, we're told that 1 - X^2 >= 0. We're asked for ALL of the possible values that fit this inequality.

The 'easiest' value that most Test Takers would immediately 'see' is 1 (since 1 - 1^2 = 0), so X COULD be 1.

Next, since we're dealing with a squared term, -1 would also be a solution (since 1 - [-1]^2 = 0).

So we immediately have at least two solutions: 1 and -1. We can eliminate Answers A, B and C.

For the last step, we have to determine what OTHER solutions are possible. You can either prove that fractions fit (try using X = 1/2) or proving that larger integers do NOT fit (try using X = 2). Either way, you can eliminate the final incorrect answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 07 Nov 2016, 16:20
Walkabout 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


We are given that 1–x^2 >= 0 and need to determine an answer that describes all values of x. Let’s isolate x in our inequality.

1–x^2 ≥ 0

1 ≥ x^2

Taking the square root of both sides of the inequality gives us:

1 ≥ x

x ≤ 1

OR

1 ≥ - x

-1 ≤ x

Thus, -1 ≤ x ≤ 1.

Answer: E
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2313
Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 10 Nov 2016, 22:19
1
Walkabout 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



In such inequalities, as long as one can factorize the expression into linear factors, the most methodical way to approach such questions is to use the wavy line approach.

You can refer to the following posts for a comprehensive treatment of the Wavy Line Approach:

http://gmatclub.com/forum/inequalities-trick-91482-80.html?sid=fde22066899cf98d261c2d987caa4509#p1465609

http://gmatclub.com/forum/wavy-line-method-application-complex-algebraic-inequalities-224319.html


Let’s apply this approach in the given question.

Given:

\(1–x^2 \geq{0}\)
\(x^2 – 1 \leq{0}\)

\((x + 1)*(x – 1) \leq{0}\) ………… (1)

Approach:

Apply the wavy line approach.


    Mark the zero points on the number and draw the wavy line.
    Identify the \(+ve\) and \(-ve\) regions of the curve.
    Since we need the range of values of \(x\), for which the expression in (1) is less than or equal to zero, we consider the \(-ve\) region(s) along with the zero points.

Working Out:

Image

The range of values of \(x\) for which the given inequality is satisfied is \(-1 \leq x \leq 1\)

Correct Answer: Option E
_________________








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 | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
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 | Inequalities

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9165
Premium Member
Re: Which of the following describes all values of x for which 1  [#permalink]

Show Tags

New post 07 Mar 2018, 18:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Which of the following describes all values of x for which 1 &nbs [#permalink] 07 Mar 2018, 18:21
Display posts from previous: Sort by

Which of the following describes all values of x for which 1

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


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®.