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# Which of the following values of x satisfy both inequalities

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Which of the following values of x satisfy both inequalities [#permalink]

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29 Nov 2012, 10:25
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(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
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jun 2013, 05:46, edited 2 times in total.
Renamed the topic.

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Posts: 42249

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Re: Which of the following values of x satisfy both inequalities [#permalink]

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29 Nov 2012, 10:37
Expert's post
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(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.

Answer: C.

Solving inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html
xy-plane-71492.html
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Kudos [?]: 132595 [0], given: 12326

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Joined: 26 Jul 2012
Posts: 6

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Re: Which of the following values of x satisfy both inequalities [#permalink]

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01 Dec 2012, 05:01
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.

Answer: C.

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

Kudos [?]: [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132595 [0], given: 12326

Re: Which of the following values of x satisfy both inequalities [#permalink]

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01 Dec 2012, 06:06
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.

Answer: C.

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.
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Re: Which of the following values of x satisfy both inequalities [#permalink]

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19 May 2016, 05:26
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).

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Location: United States
GMAT 1: 660 Q49 V31
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Re: Which of the following values of x satisfy both inequalities [#permalink]

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19 May 2016, 09:29
Backsolving was quick

C satisfies the equation
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I welcome critical analysis of my post!! That will help me reach 700+

Kudos [?]: 433 [0], given: 69

Re: Which of the following values of x satisfy both inequalities   [#permalink] 19 May 2016, 09:29
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# Which of the following values of x satisfy both inequalities

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