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Which of the foll inequalities has a solution set that, when

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Which of the foll inequalities has a solution set that, when [#permalink]

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New post 04 Aug 2008, 18:49
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Which of the foll 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

detailed soln reqd

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New post 04 Aug 2008, 19:02
E

a) x can be anything that is not between 1 and -1.
b) This one. Any number <= 3 will satify. to -infinity
c) Anything >= 4 satisfies to + infinity
d) This is actually 2 segments of lines. x can must be between +5 and -5, so it's finite in that respect, but then x = 1.99 or -1.99 doesn't fit so there is a gap between -2 and +2
e) solve for x

2<= x <= 10/3

Because there are not absolute values or exponents, we don't have to deal with negative numbers. THis is simply between 2 and 10/3. One solid, finite line.

arjtryarjtry wrote:
Which of the foll 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

detailed soln reqd

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Re: GMAT PREP [#permalink]

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New post 04 Aug 2008, 19:04
arjtryarjtry wrote:
Which of the foll 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

detailed soln reqd


e is the answer.

call inf=infinity
solution for a : x>=1 or x<=-1. so graph is broken between -1 and 1, and beyond those it is infinite. (-inf, -1] [1 inf)
solution for b : x<=3 so graph is infinite between (-inf, 3]
solution for c : x>=4 or x<=-4 same as a. (-inf, 4] and [4, inf) in between graph is broken.
solution for d : [-5,-2] and [2,5]. graph if finite but broken between -2 and 2

solution for e : [-2/3, 2/3] . graph continuous in this range. So e is the answer.

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Re: GMAT PREP [#permalink]

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New post 05 Aug 2008, 00:03
arjtryarjtry wrote:
Which of the foll 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

detailed soln reqd


IMO E) . It is a linear eqn which solves to definite single range of x.

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Re: GMAT PREP [#permalink]

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New post 05 Aug 2008, 18:50
arjtryarjtry wrote:
Which of the foll 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

detailed soln reqd

value of x should be bounded i.e,higher and lower limits should be there then only finite line segment.Hence Eliminate A,B,C where either x is > finite value or < some value

Consider D and E :
(d)2<=|x|<=5
x<=5,x>=-5 and also x>=2 and x<=-2
=>two sets of values : x>=-5 or x<=-2 and x>=2 or x<=5

(D) two line segments hence eliminate
(E) This is the only option left hence correct ,we can solve this

x>=-2/3 ,x<=2/3
hence finite line segment
IMO E :-D
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Re: GMAT PREP   [#permalink] 05 Aug 2008, 18:50
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Which of the foll inequalities has a solution set that, when

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