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Inequality problem

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by pradeepss » Sat Aug 17, 2013 10:38 pm
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 power 4 >= 1
B. X power 3 <= 27
C. X power 2 >= 16
D. 2 <= |X| <= 5
E. 2 <= 3X + 4 <= 6

I choose D which is wrong. Can someone explain?
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by Uva@90 » Sun Aug 18, 2013 12:00 am
pradeepss 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 power 4 >= 1
B. X power 3 <= 27
C. X power 2 >= 16
D. 2 <= |X| <= 5
E. 2 <= 3X + 4 <= 6

I choose D which is wrong. Can someone explain?
Hi Pradeepss,
Is Answer E which is of finite length between [spoiler]-2/3 to 2/3[/spoiler]

Regards,
Uva.
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by GMATGuruNY » Sun Aug 18, 2013 2:42 am
ccassel 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?

1. x�> 1
2. x³ ≤ 27
3. x² ≥ 16
4. 2 ≤ |x| ≤ 5
5. 2 ≤ 3x+4 ≤ 6
The equation of a line generally doesn't include exponents or absolute value.
Thus, the most linear-looking answer choice is E:

Answer choice E: 2 ≤ 3x+4 ≤ 6
Subtract 4 from each part:
-2 ≤ 3x ≤ 2
Divide each part by 3:
-2/3 ≤ x ≤ 2/3.

-2/3 ≤ x ≤ 2/3 includes every value between -2/3 and 2/3, inclusive.
This range has two ENDPOINTS: -2/3 and 2/3.
Thus, when graphed on the number line, the solution set will yield a line segment with these two endpoints -- in other words, a line segment of FINITE LENGTH.

The correct answer is E.
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by pradeepss » Sun Aug 18, 2013 12:02 pm
"The equation of a line generally doesn't include exponents or absolute value. "
[/quote]

Indeed correct answer is E. I am still confused why |X| is not correct choice.
since X can take value from -3 to 5. Its a finite length of segment. Can you guys clear my confusion?
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by GMATGuruNY » Sun Aug 18, 2013 12:23 pm
pradeepss wrote:I am still confused why |X| is not correct choice.
since X can take value from -3 to 5. Its a finite length of segment. Can you guys clear my confusion?
D: 2 ≤ |x| ≤ 5
Plotting this inequality on a number line, we get TWO valid ranges:
.....-5<----->-2...........2<----->5.....
The result is TWO finite line segments (from -5 to -2 and from 2 to 5).
Since the question stem requires that a SINGLE finite line segment be yielded, eliminate D.
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by tarik » Mon Aug 19, 2013 4:13 pm
I chose answer E. I directly eliminate answers A, B and C because there an infinite number of solutions.
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