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PS (gmatprep1) -- inequalities

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PS (gmatprep1) -- inequalities [#permalink] New post 02 Mar 2009, 19:47
00:00
A
B
C
D
E

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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
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Re: PS (gmatprep1) -- inequalities [#permalink] New post 03 Mar 2009, 02:34
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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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Re: PS (gmatprep1) -- inequalities [#permalink] New post 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.
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Re: PS (gmatprep1) -- inequalities [#permalink] New post 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..?
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Re: PS (gmatprep1) -- inequalities [#permalink] New post 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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Re: PS (gmatprep1) -- inequalities [#permalink] New post 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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Re: PS (gmatprep1) -- inequalities [#permalink] New post 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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Re: PS (gmatprep1) -- inequalities [#permalink] New post 04 Mar 2009, 13:00
thanks a lot Walker..
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which of the following inequalities [#permalink] New post 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
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Re: which of the following inequalities [#permalink] New post 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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