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Which of the following expressions is defined for all
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06 Sep 2008, 10:31
Which of the following expressions is defined for all integer values of z, such that (z^2) <9? I. (z+1)/z II. (z4)/(z^24z+4) III. 18/(z^24z5) a) None b) I only c) II only d) III only e) II and III *** What confuses me is z<3 and z<3. Am I taking the right approach? == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



Director
Joined: 12 Jul 2008
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Re: Math Question
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06 Sep 2008, 10:40
HVD1975 wrote: Which of the following expressions is defined for all integer values of z, such that (z^2) <9? I. (z+1)/z II. (z4)/(z^24z+4) III. 18/(z^24z5)
a) None b) I only c) II only d) III only e) II and III
*** What confuses me is z<3 and z<3. Am I taking the right approach? I get A The question is asking which expressions, I, II, and/or III, are defined. Each of these expressions are undefined when their denominators are 0. The prompt gives the restriction that z^2 < 9, which means 3 < z < 3 I. The expression is undefined when z = 0. II. The expression is undefined when z^24z+4 = 0 (z2)^2 = 0 z = 2 III. The expression is undefined when z^24z5 = 0 (z5)(z+1) = 0 z = 5 or 1



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Re: Math Question
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06 Sep 2008, 10:41
HVD1975 wrote: Which of the following expressions is defined for all integer values of z, such that (z^2) <9? I. (z+1)/z II. (z4)/(z^24z+4) III. 18/(z^24z5)
a) None b) I only c) II only d) III only e) II and III
*** What confuses me is z<3 and z<3. Am I taking the right approach? E if z = 0, equation 1 is undefined



VP
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Re: Math Question
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06 Sep 2008, 10:59
HVD1975 wrote: Which of the following expressions is defined for all integer values of z, such that (z^2) <9? I. (z+1)/z II. (z4)/(z^24z+4) III. 18/(z^24z5)
a) None b) I only c) II only d) III only e) II and III
*** What confuses me is z<3 and z<3. Am I taking the right approach? z ^ 2 < 9 is a quadratic inequality z ^2 9 < 0 (z3) < 0 & (z+3 ) > 0 means z<3 and z > 3 > 3 < z < 3 or (z3) > 0 & (z+3) <0 z> 3 or z < 3 means z is between [ infinity, 3] and [3, Infinity] I am guessing that we ignore the second one because this graph is a parabola and we are only concerned with the points at which it cuts the x axis. Hence we ignore the second set. The rest of the solution is already explained.



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Re: Math Question
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06 Sep 2008, 11:16
But why 3<z<3 and not z<3 and z<3
1. If z<3 then z could be 2,1,0,1,2,3,4,5, etc 2. If z<3 then z could be 4,5,6, etc
Shouldn't z<3 cancels the other integers less than 3 (2,1,0,etc)?



Director
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Re: Math Question
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06 Sep 2008, 12:08
HVD1975 wrote: But why 3<z<3 and not z<3 and z<3
1. If z<3 then z could be 2,1,0,1,2,3,4,5, etc 2. If z<3 then z could be 4,5,6, etc
Shouldn't z<3 cancels the other integers less than 3 (2,1,0,etc)? The prompt says z^2 < 9 If z < 3, then z^2 > 9.



VP
Joined: 17 Jun 2008
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Re: Math Question
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07 Sep 2008, 23:52
Very good question. Initially, I thought something is missing in the question..



Senior Manager
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Re: Math Question
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08 Sep 2008, 14:46
A
divide by 0 is never defined !



Manager
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Re: Math Question
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08 Sep 2008, 15:39
Answer should be e. x^2 < 9 ... only 2,1,0,1,2 statisfy this condition. and 0 does not satisfy the first option. so that is not defined for all x^2<9 2 and 3 are good. e. == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.




Re: Math Question &nbs
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08 Sep 2008, 15:39






