Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 03:39 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which of the following values of x satisfy both inequalities

Author Message
TAGS:

### Hide Tags

Intern  Joined: 24 Nov 2012
Posts: 23
Which of the following values of x satisfy both inequalities  [#permalink]

### Show Tags

4 00:00

Difficulty:   25% (medium)

Question Stats: 80% (01:52) correct 20% (02:19) wrong based on 238 sessions

### HideShow timer Statistics (x —1)(x + 3) > 0
(x +5)(x—4) < 0

Which of the following values of x satisfy both inequalities shown?

I. -6
II. -4
III. 2
IV. 5

A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV

Originally posted by ritumaheshwari02 on 29 Nov 2012, 10:25.
Last edited by Bunuel on 17 Jun 2013, 05:46, edited 2 times in total.
Renamed the topic.
Math Expert V
Joined: 02 Sep 2009
Posts: 56268
Re: Which of the following values of x satisfy both inequalities  [#permalink]

### Show Tags

1
1
(x —1)(x + 3) > 0
(x +5)(x—4) < 0

Which of the following values of x satisfy both inequalities shown?

I. -6
II. -4
III. 2
IV. 5

A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV

(x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.

Among choices only -4 and 2 satisfy both inequalities.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html
xy-plane-71492.html
_________________
Intern  Joined: 26 Jul 2012
Posts: 6
Re: Which of the following values of x satisfy both inequalities  [#permalink]

### Show Tags

Bunuel wrote:
(x —1)(x + 3) > 0
(x +5)(x—4) < 0

Which of the following values of x satisfy both inequalities shown?

I. -6
II. -4
III. 2
IV. 5

A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV

(x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.

Among choices only -4 and 2 satisfy both inequalities.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html
xy-plane-71492.html

Hi Bunuel,

What is the underlying concept to solve these types of inequalities ? When (x - 1)(x + 3) > 0 , we can assume that either both entities are negative or positive. You seem to have assumed both x-1 and x +3 to be positive. Please do let me know where I'm going wrong in in analysing your solution.

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 56268
Re: Which of the following values of x satisfy both inequalities  [#permalink]

### Show Tags

kheba wrote:
Bunuel wrote:
(x —1)(x + 3) > 0
(x +5)(x—4) < 0

Which of the following values of x satisfy both inequalities shown?

I. -6
II. -4
III. 2
IV. 5

A. I and II only
B. I and III only
C. II and III only
D. II and IV only
E. I, II, III, and IV

(x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.

Among choices only -4 and 2 satisfy both inequalities.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html
xy-plane-71492.html

Hi Bunuel,

What is the underlying concept to solve these types of inequalities ? When (x - 1)(x + 3) > 0 , we can assume that either both entities are negative or positive. You seem to have assumed both x-1 and x +3 to be positive. Please do let me know where I'm going wrong in in analysing your solution.

Thanks

Concept is explained in the topics given in my previous post.
_________________
Current Student Joined: 18 Oct 2014
Posts: 830
Location: United States
GMAT 1: 660 Q49 V31 GPA: 3.98
Re: Which of the following values of x satisfy both inequalities  [#permalink]

### Show Tags

Backsolving was quick C satisfies the equation
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Non-Human User Joined: 09 Sep 2013
Posts: 11668
Re: Which of the following values of x satisfy both inequalities  [#permalink]

### Show Tags

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 values of x satisfy both inequalities   [#permalink] 24 Dec 2018, 11:38
Display posts from previous: Sort by

# Which of the following values of x satisfy both inequalities  