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# Which of the following inequalities has a solution set that

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Intern
Joined: 03 Nov 2011
Posts: 8
Location: United States
Which of the following inequalities has a solution set that [#permalink]

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Updated on: 14 Apr 2012, 11:00
5
21
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:51) correct 30% (01:41) wrong based on 1031 sessions

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Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4
B. x^2>=4
C. x^3>=64
D. |x|>=4
E. |x|<=4

Originally posted by rpamecha on 14 Apr 2012, 06:43.
Last edited by Bunuel on 14 Apr 2012, 11:00, edited 3 times in total.
Edited the question
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Joined: 13 Mar 2012
Posts: 298
Concentration: Operations, Strategy
Re: Which of the following inequalities has a solution set...... [#permalink]

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14 Apr 2012, 07:46
3
rpamecha wrote:
Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

1) x>=4
2) x^2>=4
3) x^3>=64
4) |x|>=4
5) |x|<=4

OA to follow, after some discussion.

its 5).
-4 <= x<= 4

rest of the solution sets are not finite
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Joined: 02 Sep 2009
Posts: 46164
Re: Which of the following inequalities has a solution set that [#permalink]

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14 Apr 2012, 11:16
11
15
Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4 --> this inequality clearly has one infinite solution set:
Attachment:

A..gif [ 978 Bytes | Viewed 16145 times ]

B. x^2>=4 --> this inequality has two infinite solution sets, $$x\leq{-2}$$ and $$x\geq{2}$$:
Attachment:

B..gif [ 1.02 KiB | Viewed 16136 times ]

C. x^3>=64 --> this inequality has one infinite solution set, $$x\geq{4}$$:
Attachment:

C..gif [ 978 Bytes | Viewed 16139 times ]

D. |x|>=4 --> this inequality has two infinite solution sets, $$x\leq{-4}$$ and $$x\geq{4}$$:
Attachment:

D..gif [ 992 Bytes | Viewed 16135 times ]

E. |x|<=4 --> this inequality has one finite solution set, $$-4\leq{x}\leq{4}$$:
Attachment:

E..gif [ 681 Bytes | Viewed 16137 times ]

Similar question to practice: which-of-the-following-inequalities-has-a-solution-set-that-127820.html

Hope it helps.
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Re: Which of the following inequalities has a solution set that [#permalink]

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27 Jun 2012, 11:36
rpamecha wrote:
Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4
B. x^2>=4
C. x^3>=64
D. |x|>=4
E. |x|<=4

The best way to solve this problem is to do so using number lines.
a) Infinite
b) |x|>=2 which means x>=2 and x<=-2. Infinitite in opposite directions.
c) x>=4 Infinite
d) x>=4 and x<=-1 Infinite in opposite directions
e) x<=4 and x>=-4 which means -4<=x<=4. !!!

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Posts: 46164
Re: Which of the following inequalities has a solution set that [#permalink]

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17 Jun 2013, 05:51
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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Re: Which of the following inequalities has a solution set that [#permalink]

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01 Jul 2013, 07:59
Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4
B. x^2>=4
C. x^3>=64
D. |x|>=4
E. |x|<=4

Running through the list, it's pretty easy to rule out A, B, C

Let's try D
|x|>=4

x≥4
OR
-x≥4 ===> x≤-4
In other words, x may be greater than four (going from left to infinity on the number line) or it could be less than negative four (going from right to negative infinity on the number line)
INCORRECT

|x|<=4
x≤4
-x≤4 ===> x≥-4

So:
-4≤x≤4
In other words, x could be between -4 and 4 on the number line.

(E)
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Which of the following inequalities has a solution set that [#permalink]

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04 Nov 2015, 10:53
rpamecha wrote:
Which of the following inequalities has a solution set that, when graphed on a number line, is a single, finite line segment?

A. x>=4
B. x^2>=4
C. x^3>=64
D. |x|>=4
E. |x|<=4

Checking Options:

A. x>=4 i.e. Single Line segment of Infinite length to the right of 4 on Number Line

B. x^2>=4 i.e. x>=2 or x <=-2 i.e. Two Line segment of Infinite length to the right of 2 and to the left of -2 on Number Line

C. x^3>=64 i.e. x >=4 i.e. Single Line segment of Infinite length to the right of 4 unit on Number Line

D. |x|>=4 i.e. x >=4 or x <=-4 i.e. Two Line segments of Infinite length to the right of 4 and left of -4 on Number Line

E. |x|<=4 i.e. Single Line segment of FINITE length from -4 to +4 on Number Line with length of 8 units

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Re: Which of the following inequalities has a solution set that [#permalink]

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19 Jan 2018, 07:00
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.
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Re: Which of the following inequalities has a solution set that   [#permalink] 19 Jan 2018, 07:00
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