NEW HERE? LEARN MORE
closeclose
Last visit was: 14 May 2024, 13:20 It is currently 14 May 2024, 13:20
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

Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm

 1   2   
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10058 [1]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 05:58
1
Kudos
Expert Reply
Is \(4^{\frac12}+4^{\frac13}+4^{\frac14}\) greater than 5?

I'm interested in the fastest approach. So, don't forget to start your timer :wink:



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
chica
Intern
Intern
Joined: 19 Dec 2007
Posts: 39
Own Kudos [?]: 79 [1]
Given Kudos: 0
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 06:46
1
Kudos
4^1/2 + 4^1/3 + 4^1/4 = 2 + 2*4^2/3 + 2*2 = 2(1 + 4^2/3 + 2) > 5

How much time would be fast enough for the question?
User avatar
abhijit_sen
Senior Manager
Senior Manager
Joined: 10 Sep 2007
Posts: 458
Own Kudos [?]: 940 [1]
Given Kudos: 0
 Q50  V34
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 07:14
1
Kudos
chica wrote:
4^1/2 + 4^1/3 + 4^1/4 = 2 + 2*4^2/3 + 2*2 = 2(1 + 4^2/3 + 2) > 5

How much time would be fast enough for the question?

4^1/4 Is not 2*2, it is Sqrt(2).
So your calculation is bit flawed.

And this value will be slightly lesser than 5 and not greater than 5.
User avatar
abhijit_sen
Senior Manager
Senior Manager
Joined: 10 Sep 2007
Posts: 458
Own Kudos [?]: 940 [1]
Given Kudos: 0
 Q50  V34
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 07:17
1
Kudos
You can solve this question by use of Geometric Progress.
In this series a = 4^1/2, r = 4^1/3/4^1/2, and n=3
Then use Sum of GP formula and you have the answer.
This should take less than a minute.
User avatar
bmwhype2
VP
VP
Joined: 21 Jan 2007
Posts: 1346
Own Kudos [?]: 5024 [0]
Given Kudos: 4
Location: New York City
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 07:23
abhijit_sen wrote:
You can solve this question by use of Geometric Progress.
In this series a = 4^1/2, r = 4^1/3/4^1/2, and n=3
Then use Sum of GP formula and you have the answer.
This should take less than a minute.

can you elaborate?
User avatar
abhijit_sen
Senior Manager
Senior Manager
Joined: 10 Sep 2007
Posts: 458
Own Kudos [?]: 940 [0]
Given Kudos: 0
 Q50  V34
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 08:19
Sum of a GP = a(1-r^n)/(1-r)
Where a, r, and n I have already explained.

If GP is infinitely long then sum is = a/(1-r)
User avatar
GMATBLACKBELT
VP
VP
Joined: 29 Mar 2007
Posts: 1150
Own Kudos [?]: 1739 [1]
Given Kudos: 0
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 08:37
1
Kudos
walker wrote:
Is \(4^{\frac12}+4^{\frac13}+4^{\frac14}\) greater than 5?

I'm interested in the fastest approach. So, don't forget to start your timer :wink:


I didn't really have a fast approach just an approximation.

We get 2+ 4^1/3 + sqrt2

sqrt2 ~1.41....

So we have 3.41.... + 4^1/3. 4^1/3~ 1.6 would be my guess.

So its greater than 5 slightly.
User avatar
sreehari
Manager
Manager
Joined: 15 Aug 2007
Posts: 89
Own Kudos [?]: 166 [1]
Given Kudos: 0
Schools:Chicago Booth
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 08:40
1
Kudos
abhijit_sen wrote:
Sum of a GP = a(1-r^n)/(1-r)
Where a, r, and n I have already explained.

If GP is infinitely long then sum is = a/(1-r)


I don' believe you can use GP formula here... if a,b,c are in geometric progression then r=b/a=c/b

So above series is actually not in GP.
User avatar
FN
Current Student
Joined: 28 Dec 2004
Posts: 1581
Own Kudos [?]: 643 [1]
Given Kudos: 2
Location: New York City
Concentration: Social Enterprise
Schools:Wharton'11 HBS'12
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   Updated on: 25 Mar 2008, 10:25
1
Kudos
umm..it cant be greater than 5..

and its very quick to see why

4^1/2=2

4^1/3=sqrt(2)=1.58
4^1/4=sqrt(1.41) ~1.2

2+1.4=3.4+1.2=4.99 which is less than 5

you can also use the GP series too..

Originally posted by FN on 25 Mar 2008, 10:23.
Last edited by FN on 25 Mar 2008, 10:25, edited 1 time in total.
User avatar
terp26
Current Student
Joined: 22 Oct 2006
Posts: 1212
Own Kudos [?]: 351 [1]
Given Kudos: 12
Schools:Chicago Booth '11
 Q50  V38
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 10:25
1
Kudos
it's greater than 5, if you use a calculator you can see how. However only by a small fraction.
User avatar
abhijit_sen
Senior Manager
Senior Manager
Joined: 10 Sep 2007
Posts: 458
Own Kudos [?]: 940 [0]
Given Kudos: 0
 Q50  V34
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 10:31
sreehari wrote:
abhijit_sen wrote:
Sum of a GP = a(1-r^n)/(1-r)
Where a, r, and n I have already explained.

If GP is infinitely long then sum is = a/(1-r)


I don' believe you can use GP formula here... if a,b,c are in geometric progression then r=b/a=c/b

So above series is actually not in GP.


Thanks sree for pointing out my mistake. This is not a GP series although it does shows a resemblence to it. But It is still less than 5.
User avatar
GMATBLACKBELT
VP
VP
Joined: 29 Mar 2007
Posts: 1150
Own Kudos [?]: 1739 [1]
Given Kudos: 0
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   25 Mar 2008, 12:58
1
Kudos
fresinha12 wrote:
umm..it cant be greater than 5..

and its very quick to see why

4^1/2=2

4^1/3=sqrt(2)=1.58
4^1/4=sqrt(1.41) ~1.2

2+1.4=3.4+1.2=4.99 which is less than 5

you can also use the GP series too..



Its not the sqrt of (1.41) but rather the sqrt of 2.
User avatar
sondenso
Director
Director
Joined: 04 May 2006
Posts: 866
Own Kudos [?]: 6828 [0]
Given Kudos: 1
Concentration: Finance
Schools:CBS, Kellogg
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   31 Mar 2008, 02:47
walker wrote:
Is \(4^{\frac12}+4^{\frac13}+4^{\frac14}\) greater than 5?

I'm interested in the fastest approach. So, don't forget to start your timer :wink:


Walker, yesterday I cautht this problem and I chose wrong AC. Can you stimulate your approach?

Thanks,
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10058 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   31 Mar 2008, 06:12
Expert Reply
Actually, my approach is not so fast and I hoped that anybody would give the best way...

my logic:
let assume that 4^1/2 + 4^1/3 + 4^1/4 > 5
2 + 4^1/3 + 1.4142 > 5
4^1/3 > 1.5858
4 > 1.5858^3

Now I used the formula (a+b)^3=a^3 - 3*a^2*b (at b~0)

4 > (1.6-0.0142)^3 ~ 1.6^3 - 3*1.6^2*0.0142
4 > 0.001*(256*4*4) - 3*2.56*0.0142 ~4.096 - 2.56*0.0426 ~ 4.096 - 0.11 ~ 3.99

So, the assumption was correct and the expression is greater than 5

Any fresh thoughts? :)
User avatar
alpha_plus_gamma
Senior Manager
Senior Manager
Joined: 14 Aug 2007
Posts: 300
Own Kudos [?]: 583 [1]
Given Kudos: 0
Concentration: MC, PE, VC
 Q50  V37
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   31 Mar 2008, 06:36
1
Kudos
walker wrote:
Is \(4^{\frac12}+4^{\frac13}+4^{\frac14}\) greater than 5?

I'm interested in the fastest approach. So, don't forget to start your timer :wink:


It can not be greater than 5.

sqrt(4) =2

cubert(4) ~ 1.4

4^1/4 < 1.4

even if 4^1/4 is assumed to be 1.4 for simplicity, the sum will be max 4.8.
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10058 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   31 Mar 2008, 07:42
Expert Reply
the sum is greater than 5! You can use calculator to check it.
User avatar
GMAT TIGER
VP
VP
Joined: 29 Aug 2007
Posts: 1021
Own Kudos [?]: 1728 [0]
Given Kudos: 19
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   31 Mar 2008, 11:44
alpha_plus_gamma wrote:
walker wrote:
Is \(4^{\frac12}+4^{\frac13}+4^{\frac14}\) greater than 5?

I'm interested in the fastest approach. So, don't forget to start your timer :wink:


It can not be greater than 5.

sqrt(4) =2

cubert(4) ~ 1.4

4^1/4 < 1.4

even if 4^1/4 is assumed to be 1.4 for simplicity, the sum will be max 4.8.


4^(1/2) = 2.000
4^(1/3) = 1.5874
4^(1/4) = 1.41421
sum = 4^(1/2) + 4^(1/3) + 4^(1/4)
sum = 2.000 + + 1.5874 + 1.41421
sum = 5.00161 which is > 5.
User avatar
jimmyjamesdonkey
Senior Manager
Senior Manager
Joined: 01 May 2007
Posts: 484
Own Kudos [?]: 1459 [1]
Given Kudos: 0
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   31 Mar 2008, 12:47
1
Kudos
What is the source of this question?
User avatar
sondenso
Director
Director
Joined: 04 May 2006
Posts: 866
Own Kudos [?]: 6828 [0]
Given Kudos: 1
Concentration: Finance
Schools:CBS, Kellogg
Send PM
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   31 Mar 2008, 22:05
walker wrote:
Actually, my approach is not so fast and I hoped that anybody would give the best way...

my logic:
let assume that 4^1/2 + 4^1/3 + 4^1/4 > 5
2 + 4^1/3 + 1.4142 > 5
4^1/3 > 1.5858
4 > 1.5858^3

Now I used the formula (a+b)^3=a^3 - 3*a^2*b (at b~0)

4 > (1.6-0.0142)^3 ~ 1.6^3 - 3*1.6^2*0.0142
4 > 0.001*(256*4*4) - 3*2.56*0.0142 ~4.096 - 2.56*0.0426 ~ 4.096 - 0.11 ~ 3.99

So, the assumption was correct and the expression is greater than 5

Any fresh thoughts? :)


I think this question seems to be designed for you only! :P :P :P
I am lazy and not good at calculating like that. But I have no other way! :lol:

Thanks!
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10058 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink] New post   31 Mar 2008, 22:48
Expert Reply
I found a similar problem in GMATprep but the question was whether the expression is greater than 4.
So, I slightly modified the question to warm up our minds.... :roll:
GMAT Club Bot
gmatclubot
Re: Is 4^{\frac12}+4^{\frac13}+4^{\frac14} greater than 5? I'm [#permalink]
31 Mar 2008, 22:48
 1   2   
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3136 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