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# PS (gmatprep1) -- inequalities

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Director
Joined: 01 Aug 2008
Posts: 770
Followers: 4

Kudos [?]: 187 [0], given: 99

PS (gmatprep1) -- inequalities [#permalink]  02 Mar 2009, 19:47
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Difficulty:

(N/A)

Question Stats:

33% (01:01) correct 67% (01:53) wrong based on 9 sessions
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 ( x to the power of 4 is grater than equal to 1)
b) x^3 <= 27
c)x^2 >= 16
d) 2 <= |x| <= 5
e) 2<= 3x + 4 <= 6
CEO
Joined: 17 Nov 2007
Posts: 3577
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 408

Kudos [?]: 2168 [1] , given: 359

Re: PS (gmatprep1) -- inequalities [#permalink]  03 Mar 2009, 02:34
1
This post received
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Expert's post
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.
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Director
Joined: 01 Aug 2008
Posts: 770
Followers: 4

Kudos [?]: 187 [0], given: 99

Re: PS (gmatprep1) -- inequalities [#permalink]  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.
Director
Joined: 01 Aug 2008
Posts: 770
Followers: 4

Kudos [?]: 187 [0], given: 99

Re: PS (gmatprep1) -- inequalities [#permalink]  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..?
CEO
Joined: 17 Nov 2007
Posts: 3577
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 408

Kudos [?]: 2168 [0], given: 359

Re: PS (gmatprep1) -- inequalities [#permalink]  03 Mar 2009, 16:19
Expert's post
ugimba wrote:
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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Manager
Joined: 28 Jul 2004
Posts: 136
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
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Kudos [?]: 21 [0], given: 2

Re: PS (gmatprep1) -- inequalities [#permalink]  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 did you figure out the cut points for 3x+4 ?

Thanks
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kris

CEO
Joined: 17 Nov 2007
Posts: 3577
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 2168 [0], given: 359

Re: PS (gmatprep1) -- inequalities [#permalink]  04 Mar 2009, 12:23
Expert's post
krishan wrote:
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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Manager
Joined: 28 Jul 2004
Posts: 136
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
Followers: 1

Kudos [?]: 21 [0], given: 2

Re: PS (gmatprep1) -- inequalities [#permalink]  04 Mar 2009, 13:00
thanks a lot Walker..
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kris

Manager
Joined: 07 Feb 2010
Posts: 160
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Kudos [?]: 180 [0], given: 101

which of the following inequalities [#permalink]  02 Nov 2010, 05:38
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
Manager
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Posts: 225
Location: Boston
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Kudos [?]: 98 [0], given: 5

Re: which of the following inequalities [#permalink]  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   [#permalink] 02 Nov 2010, 05:45
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# PS (gmatprep1) -- inequalities

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