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:

In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

Show Tags

31 Mar 2010, 10:47

2

This post received KUDOS

31

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

58% (03:23) correct
42% (02:20) wrong based on 1040 sessions

HideShow timer Statistics

In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X^(n+2) + X^(n+3) where x is a positive integer constant. For what value of n is the ratio of An to x(1+x(1+x(1+x(1+x)))) equal to X^5?

18. In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X^(n+2) + X^(n+3) where x is a positive integer constant. For what value of n is the ratio of An to x(1+x(1+x(1+x(1+x)))) equal to X^5?

(A) 8

(B) 7

(C) 6

(D) 5

(E) 4

note: An= A sub n

Can you explain this in detail? I tried expanding out the bottom equation and solving for X to equal x^5. Didnt really work out...

Its not so hard when you realize how can you solve it, but until that, you spent half of your life.

Oh no you don't. Work smart!

\(An = x^{n-1} + x^n + x^{n+1} + x^{n+2} + x^{n+3}\) e.g. \(A2 = x + x^2 + x^3 + x^4 + x^5\) Notice you can only take x common out of all these terms i.e. the smallest term \(x^{n - 1}\)

If \(\frac{An}{{x(1+x(1+x(1+x(1+x))))}} = x^5\), it means the part: (1+x(1+x(1+x(1+x)))) will get canceled from the num and den. Ignore it. From An, you will be able to take out \(x^6\) common so that \(\frac{x^6}{x}\) gives you \(x^5\) So smallest term must be \(x^6\) i.e. \(x^{n-1}\). Therefore, n = 7.
_________________

"it means the part: (1+x(1+x(1+x(1+x)))) will get canceled from the num and den."

Regards, Subhash

\(A2 = x + x^2 + x^3 + x^4 + x^5\)

\(\frac{An}{{x(1+x(1+x(1+x(1+x))))}} = x^5\) Since the right side of the equation is just x^5, it means the entire expression: (1+x(1+x(1+x(1+x)))) should get canceled out which means we will get the same expression in the numerator as well. You don't need to do it. It is logical since otherwise, you will not get the reduced expression x^5. Also, you can see that you will get something like this in the numerator since the powers are increasing.

If you want to see it: \(A2= x( 1 + x + x^2 + x^3 + x^4) = x( 1 + x(1 + x + x^2 + x^3)) = x( 1 + x(1 + x( 1 + x + x^2))) = x( 1 + x(1 + x( 1 + x( 1 + x))))\)

omg.. by the time u read and digest the question its 1 minut e

It certainly takes you a minute or even more to get through the question and digest it but after that, it takes you less than a minute to solve it. This is true for most GMAT questions. If you understand the question well, it takes you very little time to actually solve it. If you don't understand the question well, you could end up spending 20 mins on it.
_________________

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

Show Tags

31 Jul 2012, 00:49

1

This post received KUDOS

mohankumarbd wrote:

Is this a typical 700 level GMAT question? or just an off topic question? experts pls advice.

Who can tell you? If you ask all those who took the test if they ever saw such a question on a real test, you might get the real picture...

IMO, the chance is slim that such a question will appear on a real test. It is too technical, too lengthy to be done with plugging in numbers... Until now, I didn't get the feeling that GMAT wants to test just algebraic abilities. Not that this question needs some really advanced techniques, but it's above basics...
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

In the infinite sequence A, the nth term, A(n), is given by x^(n-1) + x^n+ x^(n+1) + x^(n+2) + x^(n +3) where x is a positive integer constant. For what value of n is the ratio of A(n) to x(1+x(1+x (1+x(1+x)))) equal to x^5? (A) 8 (B) 7 (C) 6 (D) 5 (E) 4

In the infinite sequence A, the nth term, A(n), is given by x^(n-1) + x^n+ x^(n+1) + x^(n+2) + x^(n +3) where x is a positive integer constant. For what value of n is the ratio of A(n) to x(1+x(1+x (1+x(1+x)))) equal to x^5? (A) 8 (B) 7 (C) 6 (D) 5 (E) 4

Posted from my mobile device

Merging similar topics. Please ask if anything remains unclear.
_________________

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

Show Tags

24 Jul 2012, 18:27

omg.. by the time u read and digest the question its 1 minut e
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Is this a typical 700 level GMAT question? or just an off topic question? experts pls advice.

It is an algebra question that looks tricky but can be easily reasoned out. It will take you some time to understand the question but once you do, you can solve it quickly - pretty much like high level GMAT questions.
_________________

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X [#permalink]

Show Tags

05 Sep 2012, 08:02

I did it like it : as you can see x(1+x(1+x(1+x(1+x)))) X comes 5 times, therefore the max term will be X^5, in the question you see that you want to arrive at X^5 so it means that in the sum of X^n-1...x^n+3 the max term must be X^10 so that it can be x^5(x^5) therefore 10 = 3+n, n=7, timer indicate me 1min 53.

But definitely i had the answer, but i was unable to demonstrate it in that time, it would take more like 5 to 10 minutes.

gmatclubot

Re: In the infinite sequence A, An = X^(n-1) + X^n + X^(n+1) + X
[#permalink]
05 Sep 2012, 08:02

[rss2posts title=The MBA Manual title_url=https://mbamanual.com/2016/11/22/mba-vs-mim-guest-post/ sub_title=MBA vs. MiM :3qa61fk6]Hey, guys! We have a great guest post by Abhyank Srinet of MiM-Essay . In a quick post and an...

[rss2posts title=The MBA Manual title_url=https://mbamanual.com/2016/11/21/mba-vs-mim-guest-post/ sub_title=MBA vs. MiM :2kn54ay1]Hey, guys! We have a great guest post by Abhyank Srinet of MiM-Essay . In a quick post and an...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...