Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 16 Jul 2019, 09:25 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which of the following inequalities has a solution set that, when

Author Message
TAGS:

### Hide Tags

Manager  Joined: 07 Feb 2010
Posts: 124
Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

8
38 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:21) correct 28% (01:29) wrong based on 914 sessions

### HideShow timer Statistics Which of the following inequalities has a solution set that, when graphed on the number line, is a single line 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. $$2 \leq 3x+4 \leq 6$$

Attachment: Untitled.pdf [24.41 KiB]

Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: Which of the following inequalities has a solution set that  [#permalink]

### Show Tags

12
11
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.
_________________
##### General Discussion
VP  Joined: 02 Jul 2012
Posts: 1153
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42 GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Which of the following inequalities has a solution set that  [#permalink]

### Show Tags

1
3
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.
_________________
Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types
Senior Manager  Joined: 13 May 2013
Posts: 414
Re: Which of the following inequalities has a solution set that  [#permalink]

### Show Tags

2
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)
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Which of the following inequalities has a solution set that  [#permalink]

### Show Tags

1
1
Similar question to practice: http://gmatclub.com/forum/which-of-the- ... 30666.html
_________________
Intern  B
Joined: 25 Mar 2012
Posts: 4
Schools: NTU '16
Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

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.

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.

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 $$x\geq{1}$$
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

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.

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.

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 $$x\geq{1}$$.

_________________
Senior Manager  Status: The Final Countdown
Joined: 07 Mar 2013
Posts: 281
Concentration: Technology, General Management
GMAT 1: 710 Q47 V41 GPA: 3.84
WE: Information Technology (Computer Software)
Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

Bunuel , Could you please elaborate on how to solve
2 <= |x| <= 5 --> −5≤x≤−2 or 2≤x≤5

in steps..?
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

Ralphcuisak wrote:
Bunuel , Could you please elaborate on how to solve
2 <= |x| <= 5 --> −5≤x≤−2 or 2≤x≤5

in steps..?

2 <= |x| <= 5:

1. 2 <= x <= 5

2. 2 <= -x <= 5 --> multiply by -1: -2 >= x >= -5
_________________
Intern  Joined: 20 Apr 2015
Posts: 1
Re: Which of the following inequalities has a solution set that  [#permalink]

### Show Tags

1
Bunuel wrote:
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.

Dear Bunuel,

Sir , if option B is a one infinite range....then even this ans can be correct like E .
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: Which of the following inequalities has a solution set that  [#permalink]

### Show Tags

Capt wrote:
Bunuel wrote:
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.

Dear Bunuel,

Sir , if option B is a one infinite range....then even this ans can be correct like E .

How is $$-\frac{2}{3}\leq{x}\leq{\frac{2}{3}}$$ an infinite range?
_________________
Director  B
Joined: 04 Jun 2016
Posts: 562
GMAT 1: 750 Q49 V43 Which of the following inequalities has a solution set that  [#permalink]

### Show Tags

1
Which of the following inequalities has a solution set that when graphed on the number line, is a single line segment of finite length?

$$A. x^4 ≥ 1$$

$$B. x^3 ≤ 27$$

$$C. x^2 ≥ 16$$

$$D. 2≤ |x| ≤ 5$$

$$E. 2 ≤ 3x+4 ≤ 6$$

Lets check one by one
$$x^4 ≥ 1$$

Nope :- This maps to a two value of x≥1 and x ≤-1 on the number line. This is the not a finite line. This is actually an infinite line broken only from -1 to 1 but extending from -∞ to +∞

$$x^3 ≤ 27$$

Nope:- This maps to infinite values of ≤3 on the number line. This is the equation of a INFINITE line from 3 to -∞

$$x^2 ≥ 16$$

Nope :- This maps to a two value of x≥4 and x ≤-4 on the number line. This is the not a finite line. This is actually an infinite line broken only from -4 to 4 but otherwise extending from -∞ to +∞

$$2≤ |x| ≤ 5$$

Looks interesting. Lets check |X| can actually be seen as +x and also =-x
Lets check both cases individually

CASE 1) $$2≤ x≤ 5$$ This gives a finite line.

CASE 2) $$2≤ -x ≤ 5$$ or$$-5≤ x ≤ -2$$This gives a finite line again
A TOTAL OF 2 FINITE RANGES. We need only one finite range.

$$2 ≤ 3x+4 ≤ 6$$

$$x≥-\frac{2}{3}$$ and $$x≤\frac{2}{3}$$ or $$-\frac{2}{3}≤x≤\frac{2}{3}$$

YES this is a finite range from -x to +x

≥ ≤ ∞

dvinoth86 wrote:
Which of the following inequalities has a solution set that 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

_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.
Manager  B
Joined: 20 Jan 2016
Posts: 180
Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

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.

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.

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?
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

3
pra1785 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.

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.

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. Similar questions:
https://gmatclub.com/forum/which-of-the ... 27820.html (GMAT Prep).
https://gmatclub.com/forum/which-of-the ... 30666.html (Knewton).

Attachment: MSP65914h1996e60ae9h87000025b2397iibih7d09.gif [ 1 KiB | Viewed 23164 times ]

Attachment: MSP5943231f8gec7gfdfc45000012a38989ihh83g14.gif [ 1.17 KiB | Viewed 23153 times ]
Attachment: MSP5943231f8gec7gfdfc45000012a38989ihh83g14.gif [ 1.17 KiB | Viewed 23153 times ]

Attachment: MSP461h7hfif5ab0a1bfd0000250gdh577fh80424.gif [ 1.05 KiB | Viewed 23163 times ]

Attachment: MSP25821e4cg2fhi8d970g1000028dh8ii72237cfgc.gif [ 1.01 KiB | Viewed 23154 times ]

Attachment: MSP67562331eie358a08a31000017b4hh7e5e6ahiih.gif [ 967 Bytes | Viewed 5279 times ]

_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6923
Location: United States (CA)
Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

anilnandyala wrote:
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

We must determine from our answer choices which inequality is a single line segment of finite length when graphed on the number line.

A) x^4 ≥ 1

∜(x^4) ≥ ∜1

|x| ≥ 1

x ≥ 1 or x ≤ -1

Since the solution set from answer choice A produces two rays of infinite length, answer choice A is not correct.

B) x^3 ≤ 27

∛(x^3) ≤ ∛27

x ≤ 3

Since the solution set from answer choice B produces one ray of infinite length, answer choice B is not correct.

C) x^4 ≥ 16

∜(x^4) ≥ ∜16

|x| ≥ 2

x ≥ 2 or x ≤ -2

Since the solution set from answer choice C produces two rays of infinite length, answer choice C is not correct.

D) 2 ≤ |x| ≤ 5

We must solve for when x is positive and for when x is negative.

When x is positive:

2 ≤ x ≤ 5

When x is negative:

2 ≤ -x ≤ 5

-1(2 ≤ -x ≤ 5)

-2 ≥ x ≥ -5

Since the solution set from answer choice D produces two line segments of finite length, answer choice D is not correct.

Since answers A, B, C, and D are not correct, E must be the correct answer. However, for practice, we can solve it anyway.

E) 2 ≤ 3x + 4 ≤ 6

-2 ≤ 3x ≤ 2

-2/3 ≤ x ≤ 2/3

Since the solution set from answer choice E produces one line segment of finite length, answer choice E is correct.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  S
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 68
GMAT 1: 750 Q50 V42 WE: Education (Education)
Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

2
1
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
_________________
Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971568653827
Website: http://www.holamaven.com
CEO  V
Joined: 12 Sep 2015
Posts: 3847
Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

Top Contributor
1
anilnandyala wrote:
Which of the following inequalities has a solution set that, when graphed on the number line, is a single line 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. $$2 \leq 3x+4 \leq 6$$

Attachment:
Untitled.pdf

IMPORTANT
This is one of those questions that require us to check/test the answer choices. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

E) 2 ≤ 3x + 4 ≤ 6
Subtract 4 from all sides to get: -2 ≤ 3x ≤ 2
Divide all sides by 3 to get: -2/3 ≤ x ≤ 2/3
So, x can have any value from -2/3 to 2/3
So, if we were to graph the possible values of x, the line segment would have a FINITE length.

Cheers,
Brent
_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14542
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Which of the following inequalities has a solution set that, when  [#permalink]

### Show Tags

Hi All,

The equations in this question can be physically drawn or handled as a Number Property concept:

Note that the question asks for a SINGLE SEGMENT of FINITE LENGTH. This means that the group of numbers that make up the solution set would be consecutive and limited (as opposed to non-consecutive and/or infinite).

Here are the Number Properties:

A: X^4 >= 1

X can be 1, 2, 3, etc. or -1, -2, -3, etc. This group of answers is infinite and non-consecutive. Eliminate A.

B: X^3 <= 27

X can be 3, 2, 1, 0, -1, etc. This group is infinite. Eliminate B.

C: X^2 >= 16

X can be 4, 5, 6, etc. or -4, -5, -6, etc. This group is infinite and non-consecutive. Eliminate C.

D: 2 <= |X| <= 5

X can be 2, 3, 4, 5 or -2, -3, -4, -5, This group is finite BUT non-consecutive. Eliminate D.

E: 2 <= 3X + 4 <= 6

Let's simplify with algebra…

-2 <= 3X <= 2

-2/3 <= X <= 2/3

X is a finite set of answers and the answers are consecutive. This is a MATCH to what we're looking for.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Non-Human User Joined: 09 Sep 2013
Posts: 11655
Re: Which of the following inequalities has a solution set that,  [#permalink]

### Show Tags

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.
_________________ Re: Which of the following inequalities has a solution set that,   [#permalink] 07 Oct 2018, 00:33
Display posts from previous: Sort by

# Which of the following inequalities has a solution set that, when  