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

 It is currently 18 Feb 2019, 15:34

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!
• ### Get FREE Daily Quiz for 2 months

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

Buy "All-In-One Standard (\$149)", get free Daily quiz (2 mon). Coupon code : SPECIAL

# The entire range of values of x is marked by the dark region on the nu

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52938
The entire range of values of x is marked by the dark region on the nu  [#permalink]

### Show Tags

07 Nov 2016, 23:59
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:49) correct 32% (01:41) wrong based on 213 sessions

### HideShow timer Statistics

The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?

A. (3+x)(2−x) ≤ 0
B. (3−x)(2+x) ≥ 0
C. (x−3)(x+2) ≤ 0
D. (x+3)(2−x) ≥ 0
E. (3−x)(2−x) ≥ 0

Attachment:

T6774.png [ 2.39 KiB | Viewed 2302 times ]

_________________
SC Moderator
Joined: 13 Apr 2015
Posts: 1687
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: The entire range of values of x is marked by the dark region on the nu  [#permalink]

### Show Tags

08 Nov 2016, 05:36
1
2
Given: $$x \geq {-3}$$ and $$x \leq {2}$$
$$(x + 3) \geq {0}$$ and $$(x - 2) \leq {0}$$
$$(x + 3) \geq {0}$$ and $$(2 - x) \geq {0}$$

CEO
Joined: 11 Sep 2015
Posts: 3432
Re: The entire range of values of x is marked by the dark region on the nu  [#permalink]

### Show Tags

08 Nov 2016, 06:53
2
Top Contributor
Bunuel wrote:

The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?

A. (3+x)(2−x) ≤ 0
B. (3−x)(2+x) ≥ 0
C. (x−3)(x+2) ≤ 0
D. (x+3)(2−x) ≥ 0
E. (3−x)(2−x) ≥ 0

Attachment:
T6774.png

One option is to TEST some values.

According to the diagram, 0 IS a solution to the inequality. Let's test each answer choice to see whether 0 is a solution to the given inequality. If it is NOT a solution, we'll eliminate that answer choice.
A. (3+0)(2−0) = 6 BUT it is NOT the case that 6 ≤ 0 ELIMINATE A
B. (3−0)(2+0) = 6 AND it IS the case that 6 ≥ 0 KEEP B
C. (0−3)(0+2) = -6 AND it IS the case that -6 ≤ 0 KEEP C
D. (0+3)(2−0) = 6 AND it IS the case that 6 ≥ 0 KEEP D
E. (3−0)(2−0) = 6 AND it IS the case that ≥ 0 KEEP E

Test another value. According to the diagram, 3 is NOT a solution to the inequality. Let's test each remaining answer choice to see whether 3 is a solution to the given inequality. If it IS a solution, we'll eliminate it.
B. (3−3)(2+3) = 0 and it IS the case that 0 ≥ 0. So ELIMINATE B
C. (3−3)(3+2) = 0 and it IS the case that 0 ≤ 0. So ELIMINATE C
D. (3+3)(2−3) = -6 and it is NOT the case that -6 ≥ 0 KEEP D
E. (3−3)(2−3) = 0 and it IS the case that 0 ≥ 0. So ELIMINATE E

By the process of elimination, the correct answer is D

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4920
Location: United States (CA)
Re: The entire range of values of x is marked by the dark region on the nu  [#permalink]

### Show Tags

09 Nov 2016, 09:59
Bunuel wrote:

The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?

A. (3+x)(2−x) ≤ 0
B. (3−x)(2+x) ≥ 0
C. (x−3)(x+2) ≤ 0
D. (x+3)(2−x) ≥ 0
E. (3−x)(2−x) ≥ 0

Attachment:
T6774.png

Looking at the given number line, we see that the dark region on the number line represents all the values of x between -3 and 2, inclusive. In other words, it is -3 ≤ x ≤ 2. Thus:

-3 ≤ x AND x ≤ 2.

Manipulating each inequality we have:

-3 ≤ x

x ≥ -3

x + 3 ≥ 0

x ≤ 2

0 ≤ 2 - x

2 - x ≥ 0

x + 3 ≥ 0 AND 2 - x ≥ 0

The only answer choice that will satisfy both of these inequalities is (x+3)(2−x) ≥ 0.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Intern
Joined: 03 Sep 2018
Posts: 48
Re: The entire range of values of x is marked by the dark region on the nu  [#permalink]

### Show Tags

01 Feb 2019, 11:18
ScottTargetTestPrep wrote:
Bunuel wrote:

The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?

A. (3+x)(2−x) ≤ 0
B. (3−x)(2+x) ≥ 0
C. (x−3)(x+2) ≤ 0
D. (x+3)(2−x) ≥ 0
E. (3−x)(2−x) ≥ 0

Attachment:
T6774.png

Looking at the given number line, we see that the dark region on the number line represents all the values of x between -3 and 2, inclusive. In other words, it is -3 ≤ x ≤ 2. Thus:

-3 ≤ x AND x ≤ 2.

Manipulating each inequality we have:

-3 ≤ x

x ≥ -3

x + 3 ≥ 0

x ≤ 2

0 ≤ 2 - x

2 - x ≥ 0

x + 3 ≥ 0 AND 2 - x ≥ 0

The only answer choice that will satisfy both of these inequalities is (x+3)(2−x) ≥ 0.

Dear ScottTargetTestPrep,

In the last step, did you simply then multiply the two inequalities? Or how did you arrive at the conclusion that the only answer choice that will satisfy both of these inequalities is (x+3)(2−x) ≥ 0?
_________________

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4920
Location: United States (CA)
Re: The entire range of values of x is marked by the dark region on the nu  [#permalink]

### Show Tags

04 Feb 2019, 06:54
ghnlrug wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:

The entire range of values of x is marked by the dark region on the number line, as shown above. Which of the following expressions describes the range of values of x?

A. (3+x)(2−x) ≤ 0
B. (3−x)(2+x) ≥ 0
C. (x−3)(x+2) ≤ 0
D. (x+3)(2−x) ≥ 0
E. (3−x)(2−x) ≥ 0

Attachment:
T6774.png

Looking at the given number line, we see that the dark region on the number line represents all the values of x between -3 and 2, inclusive. In other words, it is -3 ≤ x ≤ 2. Thus:

-3 ≤ x AND x ≤ 2.

Manipulating each inequality we have:

-3 ≤ x

x ≥ -3

x + 3 ≥ 0

x ≤ 2

0 ≤ 2 - x

2 - x ≥ 0

x + 3 ≥ 0 AND 2 - x ≥ 0

The only answer choice that will satisfy both of these inequalities is (x+3)(2−x) ≥ 0.

Dear ScottTargetTestPrep,

In the last step, did you simply then multiply the two inequalities? Or how did you arrive at the conclusion that the only answer choice that will satisfy both of these inequalities is (x+3)(2−x) ≥ 0?

Yes, I multiplied the inequalities.
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Re: The entire range of values of x is marked by the dark region on the nu   [#permalink] 04 Feb 2019, 06:54
Display posts from previous: Sort by