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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 [#permalink] New post 03 Jan 2011, 06:06
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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
[Reveal] Spoiler: OA

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Re: which of the following inequalities has a solution that [#permalink] New post 03 Jan 2011, 06:41
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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] New post 11 Jun 2011, 21:36
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] New post 11 Jun 2011, 21:59
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] New post 13 Jul 2014, 07:34
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] New post 13 Jul 2014, 07:36
Expert's post
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}.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Which of the following inequalities has a solution set, when   [#permalink] 13 Jul 2014, 07:36
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