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:

Re: DS question on Exponents [#permalink]
11 Apr 2013, 22:09

2

This post received KUDOS

aDAMS wrote:

Q. Is x > 0?

1. x^6>x^7 2. x^7>x^8

Any number with an even exponent is \(>0\), but I wanna give you an alternative solution: 1. \(x^6>x^7\) so \(0>x^7-x^6, 0>x^6(x-1)\) at this point we can divide by x^6 because we know that does not equal 0(otherwise x^6=x^7 and not >) \(0>x-1\) and finally \(1>x\). Is x positive? it could be(0,5) or not (-1)

2.\(x^7>x^8\) becomes \(0>x^6(x^2-x)\) divide \(0>x^2-x\) so \(x(x-1)<0\) and \(0<x<1\). Is x positive? yes B _________________

It is beyond a doubt that all our knowledge that begins with experience.

1. x^6 > x^7 This option is only possible either when 1>x>0 or x<0 Like if x is <1 but >0 then the values will keep on decreasing with every increasing exponent and if x<0 then the even powers will be positive and odd ones would be -ve therefore irrespective of the value of |x| the even exponents will always be greater

2. x^7 > x^8 This is only possible when 1>x>0, as the situation would be as in case 1 but when X<0 the even exponents will always be greater

Only 2 is sufficient but 1 is not B _________________

When you feel like giving up, remember why you held on for so long in the first place.

Sorry this is probably as silly as it gets but i need help in understanding the below

In x^7 > x^8, say we divide by x^6, x> x^2 0>x(x-1) Now 0>x and 0>(x-1) for 0>x-1 ==> x <1, till here i am fine but how do we get x>0 to make 0<x<1 ?? _________________

Sorry this is probably as silly as it gets but i need help in understanding the below

In x^7 > x^8, say we divide by x^6, x> x^2 0>x(x-1) Now 0>x and 0>(x-1) for 0>x-1 ==> x <1, till here i am fine but how do we get x>0 to make 0<x<1 ??

Till here you are fine x> x^2 so \(x^2-x<0\) we have to solve this, and to solve let me use an old trick. Lets solve \(x^2-x=0,x(x-1)=0\) so x=1 or x=0. Now because the sign of x^2 is + and the operator is < we take the INTERNAL values: \(0<x<1\). Remember: to solve inequalities like this (x^2) treat them like equations (replace <,> with = ) then, once you have the results take a look at the sign of x^2 an the operator. (<,-) or (>,+) take ESTERNAL values. (if they are the "same") (>,-) or (<,+) take INTERNAL values(like this case).

Let me know if it's clear now _________________

It is beyond a doubt that all our knowledge that begins with experience.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

Every student has a predefined notion about a MBA degree:- hefty packages, good job opportunities, improvement in position and salaries but how many really know the journey of becoming...