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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.

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

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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

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

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21 Oct 2013, 09:03

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

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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?

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?

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

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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 \(x\geq{1}\)

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 \(x\geq{1}\).

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

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18 Jun 2016, 14:47

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, when [#permalink]

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09 Aug 2017, 11:32

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,

I think I am unable to understand the question here. I was between B and E and chose B because it gave one value which is 3.

I failed to understand what "a single line segment of finite length" means. Can you explain this and what we actually need to find here?

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,

I think I am unable to understand the question here. I was between B and E and chose B because it gave one value which is 3.

I failed to understand what "a single line segment of finite length" means. Can you explain this and what we actually need to find here?

\(x^3 \leq 27\) gives \(x\leq{3}\), not x = 3.

Maybe images could help:

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.

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

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15 Aug 2017, 13:34

1

This post received KUDOS

Hi, Since question is saying single line of finite length, Graph is going to be a straight line is equation is a linear equation. Linear equation is equation with highest power of variable being one. For higher powers, graph is going to be a curve. Option A has highest power of x as 4, so it is curve Option B has highest power of x as 3, so it is also curve Option C has highest power of x as 2, so it is also curve Option D has absolute function. An absolute function is combination of two functions, so it is going to give two lines. Thus option E
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