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Which of the following inequalities has a solution set, when

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

A. x^4 >= 1
B. x^3 <= 27
C. x^2 >= 16
D. 2 <= |x| <= 5
E. 2 <= 3x+4 <= 6
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anilnandyala wrote:
which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?


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

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range;

C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.
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Re: which of the following inequalities has a solution that [#permalink]

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New post 11 Jun 2011, 22:36
It is good question,
It was obvious that A,B , C are incorrect as these are exponent of X but I couldn't figure out which one between d & e is better, so attempted D on GMAT Prep test
Later, During review of the question I found that X was actually |X| - absolute value , Hence two lines,
So correct is E
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Re: which of the following inequalities has a solution that [#permalink]

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New post 11 Jun 2011, 22:59
A. x^4 ≥ 1 --> or : two infinite ranges;

B. x^3 ≤ 27 --> : one infinite range;

C. x^2 ≥ 16--> or : two infinite ranges;

D. 2 ≤ |x| ≤ 5--> or : two finite ranges;

E. 2 ≤ 3x+4 ≤ 6 -->2-4 ≤ 3x+4-4 ≤ 6-4
--> -2 ≤ 3x ≤ 2 --> -2/3 ≤x ≤ 2/3 : one finite range.
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Re: Which of the following inequalities has a solution set, when [#permalink]

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

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New post 13 Jul 2014, 08:34
Bunuel wrote:
anilnandyala wrote:
which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?


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

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range;
C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.


Hi Bunuel, for option B, why isn't it a finite range?

x^3<=27
-3<=x<=3
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Re: Which of the following inequalities has a solution set, when [#permalink]

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New post 13 Jul 2014, 08:36
russ9 wrote:
Bunuel wrote:
anilnandyala wrote:
which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?


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

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range;
C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.


Hi Bunuel, for option B, why isn't it a finite range?

x^3<=27
-3<=x<=3


x^3<=27 --> \(x\leq{3}\).
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Which of the following inequalities has a solution set, when [#permalink]

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New post 18 Feb 2015, 05:35
Bunuel wrote:
anilnandyala wrote:
which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?


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

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range;

C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.



Could someone explain Option A in detail?
I understand upon taking 4th root on both sides it becomes: x>= +-1
But, I don't understand how it gets simplified further as its been explained as: x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\)
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Re: Which of the following inequalities has a solution set, when [#permalink]

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connectvinoth wrote:
Bunuel wrote:
anilnandyala wrote:
which of the following inequalities has a solution that , when graphed on the number line is a straight line of finite length?


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

The key words in the stem are: "a single line segment of finite length"

Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have that absolute value of x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.

Answer: E.

Just to demonstrate:

A. x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\): two infinite ranges;

B. x^3 <= 27 --> \(x\leq{3}\): one infinite range;

C. x^2 >= 16 --> \(x\leq{-4}\) or \(x\geq{4}\): two infinite ranges;

D. 2 <= |x| <= 5 --> \(-5\leq{x}\leq{-2}\) or \(2\leq{x}\leq{5}\): two finite ranges;

E. 2 <= 3x+4 <= 6 --> \(-2\leq{3x}\leq{2}\) --> \(-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}\): one finite range.

Answer: E.

Hope it's clear.



Could someone explain Option A in detail?
I understand upon taking 4th root on both sides it becomes: x>= +-1
But, I don't understand how it gets simplified further as its been explained as: x^4 >= 1 --> \(x\leq{-1}\) or \(x\geq{1}\)


x >= +/- 1 does not make any sense.

When taking 4th root from both sides we'll get \(|x| \geq{1}\), which is the same as \(x\leq{-1}\) or \(x\geq{1}\).


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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

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

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New post 18 Apr 2015, 09:52
Bunuel , Could you please elaborate on how to solve
2 <= |x| <= 5 --> −5≤x≤−2 or 2≤x≤5

in steps..?
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Re: Which of the following inequalities has a solution set, when [#permalink]

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

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New post 18 Jun 2016, 14:47
Hello from the GMAT Club BumpBot!

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

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New post 05 Sep 2016, 18:23
Ralphcuisak wrote:
Bunuel , Could you please elaborate on how to solve
2 <= |x| <= 5 --> −5≤x≤−2 or 2≤x≤5

in steps..?


The absolute value of X is between 2 and 5.
X = 2 through 5
X = -2 through -5

On the number line in bold:

--|---|--0--|---|--
---2--5--0--2---5--

2 separate finite line segments.
Re: Which of the following inequalities has a solution set, when   [#permalink] 05 Sep 2016, 18:23
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