Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2015, 01:41
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What's the easiest way to solve this?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 15 Oct 2009
Posts: 12
Followers: 0

Kudos [?]: 43 [0], given: 11

What's the easiest way to solve this? [#permalink] New post 27 Mar 2010, 13:59
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:12) correct 0% (00:00) wrong based on 3 sessions
If 5^21 * 4^11 = 2 * 10^n what is the value of n?

a) 11
b) 21
c) 22
d) 23
e) 32
Senior Manager
Senior Manager
User avatar
Joined: 21 Jul 2009
Posts: 366
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Followers: 15

Kudos [?]: 117 [0], given: 22

Re: What's the easiest way to solve this? [#permalink] New post 27 Mar 2010, 14:07
Ans b.
rewrite the question statement as - 5^21 * 2^21 * 2
_________________

I am AWESOME and it's gonna be LEGENDARY!!!

Senior Manager
Senior Manager
avatar
Joined: 01 Feb 2010
Posts: 267
Followers: 1

Kudos [?]: 40 [0], given: 2

Re: What's the easiest way to solve this? [#permalink] New post 27 Mar 2010, 22:18
changhiskhan wrote:
If 5^21 * 4^11 = 2 * 10^n what is the value of n?
a) 11
b) 21
c) 22
d) 23
e) 32


5^21 * 2^(2*11) = 2*10^n
5^21 * 2^22 = 2*10^n
10^21 * 2 = 2*10^n (Multiplying 2^21 with 5^21)
so n = 21 hence B
Manager
Manager
User avatar
Joined: 26 Feb 2010
Posts: 79
Location: Argentina
Followers: 4

Kudos [?]: 7 [0], given: 1

Reviews Badge
Re: What's the easiest way to solve this? [#permalink] New post 29 Mar 2010, 11:04
changhiskhan wrote:
If 5^21 * 4^11 = 2 * 10^n what is the value of n?

a) 11
b) 21
c) 22
d) 23
e) 32


Rewriting some of the terms:
\(4^{11} = (2*2)^{11} = 2^{22}
2*10^n = 2*(2*5)^n = 2*2^n*5^n= 2^{(n+1)}\)if equal the five to five and two with two
\(5^{21} = 5^n\)and \(2^{22} = 2^{(n+1)}\)

So n must be 21
Intern
Intern
avatar
Joined: 23 Feb 2010
Posts: 14
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: What's the easiest way to solve this? [#permalink] New post 29 Mar 2010, 21:56
\(5^{21}*4^{11} = 2*10^n\)

Taking a "5" and a "4" out of their exponent sets lets me get to "2 x (2)(5)" which is starting to look like what I need:
\(5*5^{20}*4*4^{10} = 2*10^n\)
\(2*2*5*5^{20}*4^{10} = 2*10^n\)
\(2*10*5^{20}*4^{10} = 2*10^n\)

With what's left, there are two 2s in every 4. This gives me twenty 2s and twenty 5s - letting me make twenty 10s through multiplication:

\(2*10*10^{20} = 2*10^n\)

Reduce and solve for n:
\(2*10^{21} = 2*10^n\)
\(n = 21\) (b)
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 422

Kudos [?]: 2293 [0], given: 359

GMAT ToolKit User Premium Member
Re: What's the easiest way to solve this? [#permalink] New post 29 Mar 2010, 22:00
Expert's post
Another way:

The number of "5"s on the left side has to equal that on the right side: \(5^{21} = 5^n\) --> n = 21
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Re: What's the easiest way to solve this?   [#permalink] 29 Mar 2010, 22:00
    Similar topics Author Replies Last post
Similar
Topics:
Please Show me the way to solve this type of math.... aselfmademan 5 28 Oct 2011, 22:06
Faster way to solve this rates problem? Liquidus 1 24 Aug 2011, 21:00
any quick way to solve GMATD11 3 23 Mar 2011, 07:30
What is fastest way to solve this type of problem prashantbacchewar 2 15 Oct 2010, 23:23
1 Easier Way to Solve This? 12th OG Diagnostic Test #15 FlimFlam 5 25 Jan 2010, 20:14
Display posts from previous: Sort by

What's the easiest way to solve this?

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.