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1. Any expressions that contains only x in the form of |x|, x^2, x^4, x^2n are insensitive to sign of x (A,C,D in our case). Therefore, zero must satisfy such expressions, otherwise we will have at least one hole near zero and two segments. So, check x=0 for all three options. None of them fits requirement. So, A,C,D are out and B, E remain.

2. in B x=-inf satisfy the expression, so it doesn't represent finite segments.

3. Only E remains. 3x + 4 is a line cut in points x=2, and x=6 --> a finite segment.
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Re: Which of the following inequalities has a solution set, when graphed [#permalink]

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03 Mar 2009, 08:02

walker, Amazing explanation. I did follow the same way what you explained about A, C, D but I chose B and didn't realize it can satisfy infinite also ...

now it is clear to me.

(+1) kudos to you walker.

Thank you.

Last edited by ugimba on 03 Mar 2009, 08:11, edited 1 time in total.

Re: Which of the following inequalities has a solution set, when graphed [#permalink]

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03 Mar 2009, 08:06

and one more question, I made 9 mistakes in quant when I write gmatprep and still end up making 50. When I retook the exam and made just 3 mistakes only and still made 50. why it happend? it is huge range for 50 then ( from 9 mistakes to 3 mistakes in my observation)? so to get 51, there should be no wrongs at all? have to make 37 out 37 corrects..?

and one more question, I made 9 mistakes in quant when I write gmatprep and still end up making 50. When I retook the exam and made just 3 mistakes only and still made 50. why it happend? it is huge range for 50 then ( from 9 mistakes to 3 mistakes in my observation)? so to get 51, there should be no wrongs at all? have to make 37 out 37 corrects..?

A few mistakes (I had 4 mistakes in my prep and 51) at the end of the test still give you chance to get 51.
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Re: Which of the following inequalities has a solution set, when graphed [#permalink]

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04 Mar 2009, 11:51

walker wrote:

E

1. Any expressions that contains only x in the form of |x|, x^2, x^4, x^2n are insensitive to sign of x (A,C,D in our case). Therefore, zero must satisfy such expressions, otherwise we will have at least one hole near zero and two segments. So, check x=0 for all three options. None of them fits requirement. So, A,C,D are out and B, E remain.

2. in B x=-inf satisfy the expression, so it doesn't represent finite segments.

3. Only E remains. 3x + 4 is a line cut in points x=2, and x=6 --> a finite segment.

Hi Walker, could you please explain two things (sorry if they are too naive):

How do you check if "inf" satisfies an expression?

How do you check if "inf" satisfies an expression?

There is a nice concept: when x=inf (or x=-inf) there is no need to calculate complex expression. For example, y=-8x^8 + x^6 +30 x^3 +4x +2000 at x=inf (or a very huge number) we choose only the biggest power and omit all constants. So, our complex expression becomes a simple one: y = -x^8 and at x=-inf, y=-inf. And again, think about inf as a huge number, let's say 1000000000000000

krishan wrote:

How did you figure out the cut points for 3x+4 ?

y=3x+4 is a line. Just draw any line and cut it by two y=a and y=b lines (a,b - any numbers), you will get a segment.
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Re: Which of the following inequalities has a solution set, when graphed [#permalink]

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02 Nov 2010, 05:45

anilnandyala wrote:

which of the following inequalities have a solution set that , when a graphed on the number line is a single line segment of finate length

a x^4 >= 1 b x^3 <= 27 c x^2 >= 16 d 2 <= mod(x) <= 15 e 2 <= 3x+4 <= 6

E. You can easily eliminate the other four options:

A) This is true for any value of x such that \(x \leq -1\) or \(x \geq 1\) - two line segments of infinite length. B) This is true for all \(x \leq 3\) - infinite length. C) Like (A), this is true for all \(x \leq -4\) or \(x \geq 4\). D) True for \(-15 \leq x \leq -2\) or \(2 \leq x \leq 15\).

Re: Which of the following inequalities has a solution set, when graphed [#permalink]

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19 Mar 2016, 13:40

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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.

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.

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