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If N is a negative, which of the following must be true? [#permalink]
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13 Feb 2014, 08:40
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If N is a negative, which of the following must be true? I. \(N^3<N^2\) II. \(N+\frac{1}{N}<0\) III. \(N=\sqrt{N^2}\) A. I only B. II only C. III only D. I and III only E. I and II only
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Last edited by Bunuel on 13 Feb 2014, 10:31, edited 1 time in total.
Renamed the topic and edited the question.



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Re: Integer Properties [#permalink]
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13 Feb 2014, 10:28
Anasarah wrote: I was going through a manual and found the question below. I thought the answer is A but it is not.... Please help me understand why.
If N is a negative, which of the following must be true? I. N^3<N^2 II. N+1/N<0 III.N=[square_root]N^2
a. I only b.II only c.III only d.I and III only e. I and II only You figured out I and III  so will only comment on II. N is negative. 1/N is negative. Adding any two negative numbers will be negative. So N + 1/N < 0 must be true.
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Re: If N is a negative, which of the following must be true? [#permalink]
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13 Feb 2014, 10:37
Anasarah wrote: If N is a negative, which of the following must be true? I. \(N^3<N^2\) II. \(N+\frac{1}{N}<0\) III. \(N=\sqrt{N^2}\)
A. I only B. II only C. III only D. I and III only E. I and II only If N is a negative, which of the following must be true? I. \(N^3<N^2\) II. \(N+\frac{1}{N}<0\) III. \(N=\sqrt{N^2}\)A. I only B. II only C. III only D. I and III only E. I and II only I. \(N^3<N^2\). Since N is negative, then (N^3=negative) < (N^2=positive). Hence, this one must be true, II. \(N+\frac{1}{N}<0\). Both N and 1/N are negative, the sum of two negative values is negative. The same here: must be true. III. \(N=\sqrt{N^2}\). The square root function cannot give negative result: \(\sqrt{some \ expression}\geq{0}\). Negative N cannot equal to positive \(\sqrt{N^2}\). Never true. Answer: E. Hope it's clear. P.S. Please name topics properly. Check rule 3 here: rulesforpostingpleasereadthisbeforeposting133935.html Thank you.
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Re: If N is a negative, which of the following must be true? [#permalink]
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13 Feb 2014, 15:32
Bunuel, from an algebraic standpoint, if we manipulate Statement II like below, why does the inequality leave open the possibility that N^2 can be a negative fraction? I get why Neg + Neg < 0, but was wondering about the below. Thank you. N+(1/N)<0 > N<(1/N) N^2>1
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Re: If N is a negative, which of the following must be true? [#permalink]
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14 Feb 2014, 01:48
m3equals333 wrote: Bunuel, from an algebraic standpoint, if we manipulate Statement II like below, why does the inequality leave open the possibility that N^2 can be a negative fraction? I get why Neg + Neg < 0, but was wondering about the below. Thank you.
N+(1/N)<0 > N<(1/N) N^2>1 Not following you... We are asked to find which of the options must be true while given that N is negative (negative integer, negative fraction, negative irrational number). For negative N, N +1/N < 0 must be true. Can you please elaborate what you mean? Thank you.
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Re: If N is a negative, which of the following must be true? [#permalink]
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14 Feb 2014, 16:38
Sry, my question was more of a general one. Assuming n is neg, I was playing around with the inequality to see if I could manipulate it to coincide with what was already quite apparent (negative + negative = negative). Basically, I subtracted the negative fraction to the opposite side of the inequality and then multiplied the denominator to the original side (flipping the inequality in the process with N neg). I ended up with n^2 which is is presumed to be positive. Everything seemingly checks out as the inequality says n^2 is > 1, however this includes >=0 n^2 >1 as well, which seems erroneous. I was just wondering how to interpret this and if I am making any missteps in my algebraic manipulations and/or thought process. Thanks very much for your help/insight.
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Re: If N is a negative, which of the following must be true? [#permalink]
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17 Feb 2014, 07:57
m3equals333 wrote: Sry, my question was more of a general one. Assuming n is neg, I was playing around with the inequality to see if I could manipulate it to coincide with what was already quite apparent (negative + negative = negative).
Basically, I subtracted the negative fraction to the opposite side of the inequality and then multiplied the denominator to the original side (flipping the inequality in the process with N neg). I ended up with n^2 which is is presumed to be positive. Everything seemingly checks out as the inequality says n^2 is > 1, however this includes >=0 n^2 >1 as well, which seems erroneous.
I was just wondering how to interpret this and if I am making any missteps in my algebraic manipulations and/or thought process.
Thanks very much for your help/insight. I guess you want to solve for which range of n, n+1/n<0 holds true... \(n+\frac{1}{n}<0\) > \(\frac{n^2+1}{n}=\frac{positive}{n}<0\) > positive/n to be negative, n must be negative, thus \(n+\frac{1}{n}<0\) holds true for \(n<0\). Hope it helps.
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Re: If N is a negative, which of the following must be true? [#permalink]
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17 Feb 2014, 08:57
Option E. The first statement:N^3N^3=ve And N^2=+ve since square is always +ve
The second statement is also true because N+1/N=(N^2+1)/N=ve since N^2+1 will be +ve and N is given ve.
No need to look at Statement 3 since no option says all three correct.
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Re: If N is a negative, which of the following must be true? [#permalink]
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19 Feb 2014, 18:28
Yes it does, much appreciated
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Re: If N is a negative, which of the following must be true?
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