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• ### $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 Joined: 02 Dec 2012 Posts: 177 Which of the following describes all values of x for which 1 [#permalink] ### Show Tags 20 Dec 2012, 08:15 4 12 00:00 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 Joined: 02 Sep 2009 Posts: 51218 Re: Which of the following describes all values of x for which 1 [#permalink] ### Show Tags 20 Dec 2012, 08:16 4 2 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. _________________ ##### Most Helpful Community Reply Director Joined: 25 Apr 2012 Posts: 684 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, 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 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, 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 Joined: 29 Jan 2014 Posts: 4 Re: Which of the following describes all values of x for which 1 [#permalink] ### Show Tags 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 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, 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 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 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
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Re: Which of the following describes all values of x for which 1  [#permalink]

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07 Nov 2016, 16:20
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.

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Which of the following describes all values of x for which 1  [#permalink]

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10 Nov 2016, 22:19
1
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:

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

Correct Answer: Option E
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