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PS (gmatprep1) -- inequalities [#permalink]
 02 Mar 2009, 20:47
Question Stats:
33% (00:00) correct
66% (01:53) wrong based on 6 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]
03 Mar 2009, 03:34
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E1. 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]
03 Mar 2009, 09:02
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, 09:11, edited 1 time in total.
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Director
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Re: PS (gmatprep1) -- inequalities [#permalink]
03 Mar 2009, 09:06
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]
03 Mar 2009, 17:19
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]
04 Mar 2009, 12:51
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]
04 Mar 2009, 13:23
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]
04 Mar 2009, 14:00
thanks a lot Walker..
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which of the following inequalities [#permalink]
02 Nov 2010, 06:38
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]
02 Nov 2010, 06:45
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.
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Re: which of the following inequalities
[#permalink]
02 Nov 2010, 06:45
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