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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] New post 19 Feb 2012, 19:57
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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] New post 19 Feb 2012, 20:24
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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.

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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Which of the following inequalities has a solution set [#permalink] New post 29 Jan 2013, 23:55
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.


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Re: Which of the following inequalities has a solution set [#permalink] New post 30 Jan 2013, 02:58
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 that [#permalink] New post 10 Jul 2013, 09:57
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
4√x^4 ≥ 4√1
x ≥ 1
x is found anywhere from 1 to + infinity. INVALID

B. x^3 ≤ 27
3√x^3 ≤ 3√27
x ≤ 3
x is found anywhere from 3 to -infinity. INVALID

C. x^2 ≥ 16
√x^2 ≥ √16
|x| ≥ 4
x≥4 OR x≤-4
x is found anywhere from 4 to +infinity or from -4 to -infinity. INVALID

D. 2≤ |x| ≤ 5
2≤|x|
2≤x OR -2≥x
|x| ≤ 5
x≤5 OR x≥-5
This option has two segments of finite length, not one as is required by the question. INVALID

E. 2 ≤ 3x+4 ≤ 6
-2 ≤ 3x ≤ 2
(-2/3) ≤ x ≤ (2/3)
x is found anywhere from (-2/3) to (2/3). VALID

(E)
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Which of the following inequalities has a solution set such [#permalink] New post 22 Jun 2014, 16:45
Which of the following inequalities has a solution set such that, when graphed on a 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

[Reveal] Spoiler:
Answer is E, I got it wrong because of d.
Here is my rationale for why it's E, and I just want to confirm whether my reasoning is correct.

A) x>= +/- 1. +/-1 So x is greater than -1 and greater than 1 which can go to infinity, therefore not finite.
B) X <= +/-3 so x is less than -3 going to infinity. therefore not finite
C) X >= +4 / -4 Going to infinity after 4, therefore that is not the answer.
D)Taking x as positive we get range 2<=x=<5
Taking x as negative we get -2<=x=<-5
I suppose that gives us 2 finite lines and is not correct. Question asks for a SINGLE line segment, so this one is not right.
(E) 2<=3x+4 <=6
subtracting 4
-2<=3x<=2
-2/3<=x<=2/3

Answer E)

Can someone please confirm that the above logic is correct (Refer Spoiler)?

Many thanks!

Question is Discussed here : which-of-the-following-inequalities-has-a-solution-set-that-57012.html#p406630
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Re: Which of the following inequalities has a solution set such [#permalink] New post 22 Jun 2014, 20:19
Yela wrote:
Which of the following inequalities has a solution set such that, when graphed on a 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

[Reveal] Spoiler:
Answer is E, I got it wrong because of d.
Here is my rationale for why it's E, and I just want to confirm whether my reasoning is correct.

A) x>= +/- 1. +/-1 So x is greater than -1 and greater than 1 which can go to infinity, therefore not finite.
B) X <= +/-3 so x is less than -3 going to infinity. therefore not finite
C) X >= +4 / -4 Going to infinity after 4, therefore that is not the answer.
D)Taking x as positive we get range 2<=x=<5
Taking x as negative we get -2<=x=<-5
I suppose that gives us 2 finite lines and is not correct. Question asks for a SINGLE line segment, so this one is not right.
(E) 2<=3x+4 <=6
subtracting 4
-2<=3x<=2
-2/3<=x<=2/3

Answer E)

Can someone please confirm that the above logic is correct (Refer Spoiler)?

Many thanks!

Question is Discussed here : which-of-the-following-inequalities-has-a-solution-set-that-57012.html#p406630



Hi Yela,

Your logic is correct.
Ans is E

Question is Discussed here : which-of-the-following-inequalities-has-a-solution-set-that-57012.html#p406630

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Re: Which of the following inequalities has a solution set that [#permalink] New post 23 Jun 2014, 00:20
Expert's post
Yela wrote:
Which of the following inequalities has a solution set such that, when graphed on a 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

[Reveal] Spoiler:
Answer is E, I got it wrong because of d.
Here is my rationale for why it's E, and I just want to confirm whether my reasoning is correct.

A) x>= +/- 1. +/-1 So x is greater than -1 and greater than 1 which can go to infinity, therefore not finite.
B) X <= +/-3 so x is less than -3 going to infinity. therefore not finite
C) X >= +4 / -4 Going to infinity after 4, therefore that is not the answer.
D)Taking x as positive we get range 2<=x=<5
Taking x as negative we get -2<=x=<-5
I suppose that gives us 2 finite lines and is not correct. Question asks for a SINGLE line segment, so this one is not right.
(E) 2<=3x+4 <=6
subtracting 4
-2<=3x<=2
-2/3<=x<=2/3

Answer E)

Can someone please confirm that the above logic is correct (Refer Spoiler)?

Many thanks!


Merging similar topics. Please refer to the discussion above.

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

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 3, and 6. Thank you.


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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

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Re: Which of the following inequalities has a solution set that   [#permalink] 23 Jun 2014, 00:20
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