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# Which of the following inequalities has a solution set that

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Joined: 19 Oct 2011
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Which of the following inequalities has a solution set that  [#permalink]

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19 Feb 2012, 19:57
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Question Stats:

73% (01:18) correct 27% (01:28) wrong based on 632 sessions

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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

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Posts: 50627
Re: Which of the following inequalities has a solution set that  [#permalink]

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19 Feb 2012, 20:24
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10
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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Re: Which of the following inequalities has a solution set that  [#permalink]

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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.

Thanks
Mridul
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Re: Which of the following inequalities has a solution set that  [#permalink]

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30 Jan 2013, 02:58
1
1
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]

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10 Jul 2013, 09:57
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
Joined: 02 Sep 2009
Posts: 50627
Which of the following inequalities has a solution set that  [#permalink]

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23 Jun 2014, 00:20
1
1
Similar question to practice: http://gmatclub.com/forum/which-of-the- ... 30666.html
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Re: Which of the following inequalities has a solution set that  [#permalink]

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20 Apr 2015, 00:13
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
Joined: 02 Sep 2009
Posts: 50627
Re: Which of the following inequalities has a solution set that  [#permalink]

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20 Apr 2015, 03:32
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?
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Director
Joined: 04 Jun 2016
Posts: 569
GMAT 1: 750 Q49 V43
Which of the following inequalities has a solution set that  [#permalink]

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25 Jul 2016, 03:36
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

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

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