GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Mar 2020, 22:26

### 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

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

# If 9 - x^2 ≥ 0, which of the following describes all

Author Message
TAGS:

### Hide Tags

Manager
Joined: 11 Aug 2012
Posts: 107
Schools: HBS '16, Stanford '16
If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

### Show Tags

21 May 2013, 08:46
2
00:00

Difficulty:

5% (low)

Question Stats:

86% (01:04) correct 14% (01:26) wrong based on 204 sessions

### HideShow timer Statistics

If $$9 - x^2 \geq{} 0$$, which of the following describes all possible values of x ?

A. 3 ≥ x ≥ -3
B. x ≥ 3 or x ≤ -3
C. 3 ≥ x ≥ 0
D. -3 ≥ x
E. 3 ≤ x

My doubt is this:
When we solve the inequality, we get this:

x ≤ 3 ; x ≥ -3

Is x ≤ 3 AND x ≥ -3?, or
x ≤ 3 OR x ≥ -3?

In other words, should we find the intersection between those values? (In that case, it would be "AND"?

But what about if we had gotten this: x ≤ - 3 ; x ≥ 3 ? What would the answer be? x ≤ - 3 OR x ≥ 3?, or "there are no values for x"?
VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1000
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

### Show Tags

21 May 2013, 08:51
$$9 - x^2 \geq{} 0$$
$$- x^2 \geq{} -9$$
$$x^2 \leq{} 9$$

$$-3\leq{x}\leq{3}$$

danzig wrote:
My doubt is this:
When we solve the inequality, we get this:

x ≤ 3 ; x ≥ -3

Is x ≤ 3 AND x ≥ -3?, or
x ≤ 3 OR x ≥ -3?

In other words, should we find the intersection between those values? (In that case, it would be "AND"?

But what about if we had gotten this: x ≤ - 3 ; x ≥ 3 ? What would the answer be? x ≤ - 3 OR x ≥ 3?, or "there are no values for x"?

Here we take the internal values between -3 and 3. I am not sure of what you mean in your question
Check this post tips-and-tricks-inequalities-150873.html

Let me know if it remains unclear
Manager
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 113
Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
GPA: 3.5
WE: Web Development (Computer Software)
Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

### Show Tags

21 May 2013, 08:57
Please refer to the graph attached. ** Apologies for the sloppy paint work

As you can see, f(x) = x^2 - 9 = (x-3)(x+3) <=0 ***After changing sign multiply minus both sides. The only region possible would be the region between the roots of f(x) = 0 i.e.{-3,3}. Once can also go about and plot the inverted parabola for 9 - x^2 and prove the region is greater than 0 as well

Regards,
Arpan
Attachments

graph-fun.png [ 9.17 KiB | Viewed 2579 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 62287
Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

### Show Tags

22 May 2013, 01:47
danzig wrote:
If $$9 - x^2 \geq{} 0$$, which of the following describes all possible values of x ?

A. 3 ≥ x ≥ -3
B. x ≥ 3 or x ≤ -3
C. 3 ≥ x ≥ 0
D. -3 ≥ x
E. 3 ≤ x

My doubt is this:
When we solve the inequality, we get this:

x ≤ 3 ; x ≥ -3

Is x ≤ 3 AND x ≥ -3?, or
x ≤ 3 OR x ≥ -3?

In other words, should we find the intersection between those values? (In that case, it would be "AND"?

But what about if we had gotten this: x ≤ - 3 ; x ≥ 3 ? What would the answer be? x ≤ - 3 OR x ≥ 3?, or "there are no values for x"?

Check here: if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html#p731476

Hope it helps.
_________________
SVP
Joined: 23 Feb 2015
Posts: 1642
Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

### Show Tags

03 Feb 2017, 03:07
danzig wrote:
If $$9 - x^2 \geq{} 0$$, which of the following describes all possible values of x ?

A. 3 ≥ x ≥ -3
B. x ≥ 3 or x ≤ -3
C. 3 ≥ x ≥ 0
D. -3 ≥ x
E. 3 ≤ x

$$9 - x^2 \geq{} 0$$
=>9≥x^2
=> root 9≥root x^2
=> 3≥absolute value of x
absolute value of x≤3
so, if x positive, then x≤3
but, if x negative, then
-x≤3
=>x≥-3
if we combined the values of x then it will be...
3 ≥ x ≥ -3
The correct choice is A.
Thank you...
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2801
Re: If 9 - x^2 ≥ 0, which of the following describes all  [#permalink]

### Show Tags

08 Feb 2017, 18:44
danzig wrote:
If $$9 - x^2 \geq{} 0$$, which of the following describes all possible values of x ?

A. 3 ≥ x ≥ -3
B. x ≥ 3 or x ≤ -3
C. 3 ≥ x ≥ 0
D. -3 ≥ x
E. 3 ≤ x

Let’s solve the given inequality:

9 - x^2 ≥ 0

9 > x^2

√9 ≥ √x^2

3 ≥ |x|

Thus: 3 ≥ x

or

3 ≥ -x

-3 ≤ x

Finally, we can say: -3 ≤ x ≤ 3.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
197 Reviews

5-star 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.

Re: If 9 - x^2 ≥ 0, which of the following describes all   [#permalink] 08 Feb 2017, 18:44
Display posts from previous: Sort by