Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If N is a negative, which of the following must be true? [#permalink]
13 Feb 2014, 09:37

Expert's post

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.

Re: If N is a negative, which of the following must be true? [#permalink]
13 Feb 2014, 14:32

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.

Re: If N is a negative, which of the following must be true? [#permalink]
14 Feb 2014, 00:48

Expert's post

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.
_________________

Re: If N is a negative, which of the following must be true? [#permalink]
14 Feb 2014, 15:38

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.

Re: If N is a negative, which of the following must be true? [#permalink]
17 Feb 2014, 06:57

1

This post received KUDOS

Expert's post

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.