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# Which of the following inequalities has a solution set that

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Which of the following inequalities has a solution set that [#permalink]  19 Feb 2012, 20:57
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Which of the following inequalities has a solution set that when graphed on the number line, is a single 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
[Reveal] Spoiler: OA

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Re: Which of the following inequalities has a solution set that [#permalink]  19 Feb 2012, 21:24
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dvinoth86 wrote:
Which of the following inequalities has a solution set that when graphed on the number line, is a single segment of finite length?

A. x4 ≥ 1
B. x3 ≤ 27
C. x2 ≥ 16
D. 2≤ |x| ≤ 5
E. 2 ≤ 3x+4 ≤ 6

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.

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.

Hope it's clear.
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Inequalities [#permalink]  29 Oct 2012, 06:40
Could any body pls reply to this? Thanks.
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Ineq Qstn.docx [503.19 KiB]

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Re: Inequalities [#permalink]  29 Oct 2012, 06:46
chigiwigi wrote:
Could any body pls reply to this? Thanks.

Merging similar topics. Please refer to the solution above.

Similar question to practice: which-of-the-following-inequalities-has-a-solution-set-that-130666.html?hilit=solution%20graphed

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Which of the following inequalities has a solution set [#permalink]  30 Jan 2013, 00:55
Which of the following inequalities has a solution set that when graphed on the number line, is a single
segment of finite length?
A. x^4 \geq 1
B. x^3 \leq 27
C. x^2 \geq 16
D. 2\leq |x| \leq 5
E. 2 \leq 3x+4 \leq 6

Question taken from one of the Quant files in the download section at Gmatclub.

In all the above options, we are going to get graphs with range values. Does this Questions asks where the range is limited/minimum (Finite Length)

How would you solve Option D.

Thanks
Mridul
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Re: Which of the following inequalities has a solution set [#permalink]  30 Jan 2013, 03:58
mridulparashar1 wrote:
Which of the following inequalities has a solution set that when graphed on the number line, is a single
segment of finite length?
A. x^4 \geq 1
B. x^3 \leq 27
C. x^2 \geq 16
D. 2\leq |x| \leq 5
E. 2 \leq 3x+4 \leq 6

Question taken from one of the Quant files in the download section at Gmatclub.

In all the above options, we are going to get graphs with range values. Does this Questions asks where the range is limited/minimum (Finite Length)

How would you solve Option D.

Thanks
Mridul

The question asks for the option for which the range does not extend to infinity or does not have a break in between.

A) x can be any value greater than 1
B) x can be any value lesser than 3
C) x can be any value greater than 4
D) This option does have a finite range. However, there is a break inbetween for values in the range -2 < x < 2.
E) Same as -\frac{2}{3} \leq x \leq \frac{2}{3}. Finite straight line.
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Re: Which of the following inequalities has a solution set [#permalink]  30 Jan 2013, 04:18
mridulparashar1 wrote:
Which of the following inequalities has a solution set that when graphed on the number line, is a single
segment of finite length?
A. x^4 \geq 1
B. x^3 \leq 27
C. x^2 \geq 16
D. 2\leq |x| \leq 5
E. 2 \leq 3x+4 \leq 6

Question taken from one of the Quant files in the download section at Gmatclub.

In all the above options, we are going to get graphs with range values. Does this Questions asks where the range is limited/minimum (Finite Length)

How would you solve Option D.

Thanks
Mridul

Merging similar topics. Please refer to the solution above.
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Re: Which of the following inequalities has a solution set   [#permalink] 30 Jan 2013, 04:18
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