NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 02:10 It is currently 26 Apr 2024, 02:10
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

M17 # 05

User avatar
vicksikand
Senior Manager
Senior Manager
Joined: 29 Sep 2009
Posts: 335
Own Kudos [?]: 104 [0]
Given Kudos: 5
GMAT 1: 690 Q47 V38
Send PM
M17 # 05 [#permalink] New post   03 Oct 2010, 13:31
What is \(\frac{1}{2} + \left(\frac{1}{2}\right)^2 + \left(\frac{1}{2}\right)^3 + ... + \left(\frac{1}{2}\right)^{20}\) between?

(C) 2008 GMAT Club - m17#5

* \(\frac{1}{2}\) and \(\frac{2}{3}\)
* \(\frac{2}{3}\) and \(\frac{3}{4}\)
* \(\frac{3}{4}\) and \(\frac{9}{10}\)
* \(\frac{9}{10}\) and \(\frac{10}{9}\)
* \(\frac{10}{9}\) and \(\frac{3}{2}\)

This is a Geometric Progression:
First term(a) 1/2 , Common ratio(r) 1/2 and n : 20+1
Sum of a GP: a(1-r^n)/(1-r)
= 1/2 (1- (1/2)^21) / (1-1/2)
(1- (1/2)^21) should be close to 1
hence answer : 1/2(1)/(1/2) = 1 (close to 1)
D

Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
Where to now? Try our up-to-date Free Adaptive GMAT Club Tests for the latest questions.
Still interested? Check out the "Best Topics" block below for better discussion and related questions.
Thank you for understanding, and happy exploring!
User avatar
shrouded1
Retired Moderator
Joined: 02 Sep 2010
Posts: 615
Own Kudos [?]: 2931 [0]
Given Kudos: 25
Location: London
 Q51  V41
Send PM
GMAT ToolKit User Reviews Badge
Re: M17 # 05 [#permalink] New post   03 Oct 2010, 13:40
vicksikand wrote:
What is \(\frac{1}{2} + \left(\frac{1}{2}\right)^2 + \left(\frac{1}{2}\right)^3 + ... + \left(\frac{1}{2}\right)^{20}\) between?

(C) 2008 GMAT Club - m17#5

* \(\frac{1}{2}\) and \(\frac{2}{3}\)
* \(\frac{2}{3}\) and \(\frac{3}{4}\)
* \(\frac{3}{4}\) and \(\frac{9}{10}\)
* \(\frac{9}{10}\) and \(\frac{10}{9}\)
* \(\frac{10}{9}\) and \(\frac{3}{2}\)

This is a Geometric Progression:
First term(a) 1/2 , Common ratio(r) 1/2 and n : 20+1
Sum of a GP: a(1-r^n)/(1-r)
= 1/2 (1- (1/2)^21) / (1-1/2)
(1- (1/2)^21) should be close to 1
hence answer : 1/2(1)/(1/2) = 1 (close to 1)
D


Lower Bounds
First term is 1/2
If you add the first two terms, 1/2+1/4 you are above 3/4
So A & B can't be answers

Upper Bounds
If this was an infinite series, the sum would be (1/2)/(1-1/2) = 1
So this sum has to be less than 1
So E can't be the answer

Between C & D
You don't need to calculate the sum, just observe the pattern (half of the distance to 1 is always covered)
First term = 1/2
First two terms = 3/4
First three terms = 7/8
First four terms = 15/16
.. and so on ...

So it is easy to see that this sum will very quickly become greater than 9/10 (at the fourth term in fact)

So answer is (D)
User avatar
Sachin9
Senior Manager
Senior Manager
Joined: 22 Jul 2012
Status:Gonna rock this time!!!
Posts: 356
Own Kudos [?]: 166 [0]
Given Kudos: 562
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE:Information Technology (Computer Software)
Send PM
Re: M17 # 05 [#permalink] New post   20 Feb 2013, 04:44
Bunuel,
Is there any way to solve this without using the formula?

Also, is GP tested on GMAT?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619095 [0]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: M17 # 05 [#permalink] New post   26 Feb 2013, 08:19
Expert Reply
Sachin9 wrote:
Bunuel,
Is there any way to solve this without using the formula?

Also, is GP tested on GMAT?


Check here: m17q5-72268.html

Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
Where to now? Try our up-to-date Free Adaptive GMAT Club Tests for the latest questions.
Still interested? Check out the "Best Topics" block above for better discussion and related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: M17 # 05 [#permalink]
26 Feb 2013, 08:19
Moderator:
Bunuel
Math Expert
92923 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions