Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 27 Mar 2008
Posts: 60

Which of the following describes all values of x for which
[#permalink]
Show Tags
Updated on: 09 Oct 2018, 13:23
Question Stats:
73% (01:10) correct 27% (01:22) wrong based on 850 sessions
HideShow timer Statistics
Which of the following describes all values of x for which \(1x^2 ≥ 0\) ? A. x ≥ 1 B. x ≤ 1 C. 0 ≤ x ≤ 1 D. x ≤ 1 or x ≥ 1 E. 1 ≤ x ≤ 1
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by mgoblue123 on 16 Aug 2008, 11:58.
Last edited by carcass on 09 Oct 2018, 13:23, edited 3 times in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 59073

Re: Which of the following describes all values of x for which
[#permalink]
Show Tags
20 Apr 2012, 04:08
catty2004 wrote: x2suresh wrote: droopy57 wrote: Which of the following describes all values of x for which 1x^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. 1x^2 >= 0 > x^21<=0 > (x+1)(x1)<=0 Above equation true for i) x+1 <=0 and x1 >=0 > x<= 1 and x>=1 > this is not possible Strike out this solution ii) x+1 >=0 and x1 <=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: \(1x^2\geq{0}\) > \(x^2\leq{1}\), since both parts of the inequality are nonnegative then we can take square root: \(x\leq{1}\) > \(1\leq{x}\leq{1}\). Now, other approach would be: \(1x^2\geq{0}\) > \(x^21\leq{0}\) > \((x+1)(x1)\leq{0}\) > the roots are 1 and 1 > "<" sign indicates that the solution lies between the roots, so \(1\leq{x}\leq{1}\). Solving inequalities: x24x94661.html#p731476 ( check this one first) inequalitiestrick91482.htmldatasuffinequalities109078.htmlrangeforvariablexinagiveninequality109468.html?hilit=extreme#p873535everythingislessthanzero108884.html?hilit=extreme#p868863Now, about x2suresh's approach: we have \((x+1)(x1)\leq{0}\), 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 (x1) is positive and the case B. when the first multiple (x+1) is positive and the second (x1) is negative to get the range for which \((x+1)(x1)\leq{0}\) 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 (x1), the smaller number to be positive. As for case B, it gives: \(x+1\geq{0}\) and \(x1\leq{0}\) > \(x1\geq{1}\) and \(x\leq{1}\) > \(1\leq{x}\leq{1}\). Hope it helps.
_________________




Director
Joined: 25 Apr 2012
Posts: 654
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: Which of the following describes all values of x for which 1
[#permalink]
Show Tags
27 May 2014, 03:37
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 \(1x^2\geq{0}\) > \(x^2\leq{1}\) > \(1\leq{x}\leq{1}\). Answer: E. Bunuel, Can you explain how we go from \(x^2\) to x in last step Hello, You have \(1x^2\geq{0}\). Since LHS and RHS are nonnegative,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 \(1x^2\geq{0}\) or \((1x)(1+x)\geq{0}\) (using \(a^2b^2=(ab)(a+b)\) ) 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 graphicapproachtoproblemswithinequalities68037.htmlmathnumbertheory88376.htmlifxisanintegerwhatisthevalueofx1x24x94661.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.”




VP
Joined: 07 Nov 2007
Posts: 1213
Location: New York

Re: Which of the following describes all values of x for which
[#permalink]
Show Tags
16 Aug 2008, 14:49
droopy57 wrote: Which of the following describes all values of x for which 1x^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. 1x^2 >= 0 > x^21<=0 > (x+1)(x1)<=0 Above equation true for i) x+1<=0 and x1>=0 > x<= 1 and x>=1 > this is not possible Strike out this solution ii) x+1>=0 and x1<=0 > x>=1 and x<=1 > 1<=x<=1
_________________
Your attitude determines your altitude Smiling wins more friends than frowning



Intern
Joined: 30 May 2008
Posts: 46

Re: Which of the following describes all values of x for which
[#permalink]
Show Tags
20 Apr 2012, 02:18
x2suresh wrote: droopy57 wrote: Which of the following describes all values of x for which 1x^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. 1x^2 >= 0 > x^21<=0 > (x+1)(x1)<=0 Above equation true for i) x+1 <=0 and x1 >=0 > x<= 1 and x>=1 > this is not possible Strike out this solution ii) x+1 >=0 and x1 <=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?



Math Expert
Joined: 02 Sep 2009
Posts: 59073

Re: Which of the following describes all values of x for which 1
[#permalink]
Show Tags
20 Dec 2012, 09:16
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 \(1x^2\geq{0}\) > \(x^2\leq{1}\) > \(1\leq{x}\leq{1}\). Answer: E.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59073

Re: Which of the following describes all values of x for which
[#permalink]
Show Tags
17 Jun 2013, 05:51
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Intern
Joined: 24 Aug 2013
Posts: 5

Re: Which of the following describes all values of x for which 1
[#permalink]
Show Tags
27 May 2014, 02:57
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 \(1x^2\geq{0}\) > \(x^2\leq{1}\) > \(1\leq{x}\leq{1}\). Answer: E. Bunuel, Can you explain how we go from \(x^2\) to x in last step



Intern
Joined: 08 Jan 2014
Posts: 1

Re: Which of the following describes all values of x for which 1
[#permalink]
Show Tags
26 Jun 2014, 16:16
(1x^2) >= 0 can be expressed as (1x) (1+x) >=0
So 1x>=0 (OR) 1+x>=0.
Therefore, 1 >= x (OR) x >= 1



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15449
Location: United States (CA)

Re: Which of the following describes all values of x for which 1
[#permalink]
Show Tags
30 Sep 2015, 11:13
Hi All, With inequalitybased 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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2812

Re: Which of the following describes all values of x for which
[#permalink]
Show Tags
07 Jul 2016, 10:00
droopy57 wrote: Which of the following describes all values of x for which 1x^2 ≥ 0 ?
A. x ≥ 1 B. x ≤ 1 C. 0 ≤ x ≤ 1 D. x ≤ 1 or x ≥ 1 E. 1 ≤ x ≤ 1 To solve, we first isolate the x^2 in the inequality 1 – x^2 ≥ 0. So we have: 1 ≥ x^2 Next, we take the square root of both sides, to isolate x. √1 ≥ √x^2 This gives us: 1 ≥ x Because the variable x is inside the absolute value sign, we must consider that x can be either positive or negative. Therefore, we’ll need to solve the inequality twice. When x is positive: 1 ≥ x means 1 ≥ x This can be reexpressed as x ≤ 1. When x is negative: 1 ≥ x means 1 ≥ x (Divide both sides by 1 and switch the inequality sign) 1 ≤ x We combine the two resulting inequalities to get: 1 ≤ x ≤ 1 Answer is E.
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3141

Which of the following describes all values of x for which 1
[#permalink]
Show Tags
10 Nov 2016, 23:19
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/inequalitiestrick9148280.html?sid=fde22066899cf98d261c2d987caa4509#p1465609http://gmatclub.com/forum/wavylinemethodapplicationcomplexalgebraicinequalities224319.htmlLet’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: The range of values of \(x\) for which the given inequality is satisfied is \(1 \leq x \leq 1\) Correct Answer: Option E
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15449
Location: United States (CA)

Re: Which of the following describes all values of x for which
[#permalink]
Show Tags
14 Feb 2018, 16:44
Hi All, With inequalitybased 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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



NonHuman User
Joined: 09 Sep 2013
Posts: 13583

Re: Which of the following describes all values of x for which
[#permalink]
Show Tags
27 Apr 2019, 06:56
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.
_________________




Re: Which of the following describes all values of x for which
[#permalink]
27 Apr 2019, 06:56






