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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

first we know that X is negative and it's between -1 and 0,

1)x3<x2-correct because x3 is negative(---=-) and x2 is posittive(--=+) 2)x5<1-x x5 is negative and 1 minus negative gives 1+positive so it's correct 3)x4<x2 here u should remember that if number is between 0 and 1, square gives less than actual number...u can check for example 0.5 in square is 0.25 which is less than 0.5..so X4 is less than x2
_________________

As X^2 will always be positive or zero. only (X-1) contributes to the negativity of the above inequality.

(X-1) < 0 => X <1 so it must be true for X to be in range (-1,0)

(2). X^5 < 1 -X

=> X(X^4+1) < 1 => X <1 Must be true (As X^4 +1 wil always be greater than 1)

(3). X^4 < X^2

=>X^2(X^2-1) <0 => (X+1)(X-1) <0

=> -1<X<1 MUST be true

Hence , (E) !!
_________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

If -1 < x < 0, which of the following must be true?

I. x^3 < x^2 II. x^5 < 1 – x III. x^4 < x^2

A. I only B. I and II only C. II and III only D. I and III only E. I, II and III

I. x^3 < x^2 --> from -1 < x < 0 it follows that LHS<0<RHS, so this statement is true.

II. x^5 < 1 – x --> x(x^4+1) < 1 --> negative*positive < 0 < 1, so this statement is also true.

III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 0 is follows that x^2>0): x^2 < 1. Again, as -1 < x < 0, then x^2 must be less than 1. Hence, this statement is also true.

Fractions get smaller every time they are multiplied together. For negative numbers raised to an odd power the result will be negative. Knowing these two things makes the comparisons fairly simple.
_________________

I do not beg for kudos.

gmatclubot

Re: If -1 < x < 0, which of the following must be true?
[#permalink]
27 Jul 2013, 11:25

Campus visits play a crucial role in the MBA application process. It’s one thing to be passionate about one school but another to actually visit the campus, talk...

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...