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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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(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, 04:46, edited 2 times in total.
Renamed the topic.
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Re: Which of the following values of x satisfy both inequalities [#permalink]

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New post 29 Nov 2012, 09:37
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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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Re: Which of the following values of x satisfy both inequalities [#permalink]

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New post 01 Dec 2012, 04:01
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
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Re: Which of the following values of x satisfy both inequalities [#permalink]

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New post 01 Dec 2012, 05:06
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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

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New post 19 May 2016, 08:29
Backsolving was quick :)

C satisfies the equation
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Re: Which of the following values of x satisfy both inequalities   [#permalink] 19 May 2016, 08:29
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