NEW HERE? LEARN MORE
closeclose
Last visit was: 28 Apr 2024, 15:48 It is currently 28 Apr 2024, 15:48
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

crazy exponent problem

User avatar
imadummy
Intern
Intern
Joined: 31 Jul 2008
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
crazy exponent problem [#permalink] New post   31 Jul 2008, 13:13
Hi All, would someone please help explain this question? It's from GMAP Prep 1. Many thanks.

5^21 * 4^11 = 2 * 10^N
N=?



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
VPRedSoxFan
Intern
Intern
Joined: 07 May 2008
Posts: 10
Own Kudos [?]: 1 [0]
Given Kudos: 0
Send PM
Re: crazy exponent problem [#permalink] New post   31 Jul 2008, 13:15
I like this problem a lot. Hopefully I can help.

If you change the 4^11 into (2^2)^11, then it becomes 2^22.

Now, if you look at the left side, you have 21 5's being multiplied by 22 2's. If you match up a 5 and 2, you'll get 21 pairs of 5*2 with one 2 left over. Turn those 21 pairs of a 5 and 2 into 10 and you're left with 21 10's multiplied together and then multiplied by 2.

That equals 2* (10^21) so N=21.


Algebraically, (ab)^c = a^c * b^c as a rule of exponents. After changing 4^11 into 2^22 you can apply this rule backwards as 5^21 * 2^21 * 2 = (5*2)^21 * 2 = 2* (10^21), N = 21
User avatar
x2suresh
Director
Director
Joined: 07 Nov 2007
Posts: 718
Own Kudos [?]: 3077 [0]
Given Kudos: 5
Location: New York
Send PM
Re: crazy exponent problem [#permalink] New post   31 Jul 2008, 13:19
imadummy wrote:
Hi All, would someone please help explain this question? It's from GMAP Prep 1. Many thanks.

5^21 * 4^11 = 2 * 10^N
N=?


5^21 * 4^11 = 2 * 10^N
-->
5^21 * (2*2)^11 = 2 * 10^N
-->
5^21 * (2)^22 = 2 * 10^N
5^21 * (2)^21 = 10^N
(5*2)^21 = 10^N
(10)^21 = 10^N
-->N=21
User avatar
B
jallenmorris
VP
VP
Joined: 30 Apr 2008
Posts: 1230
Own Kudos [?]: 951 [0]
Given Kudos: 32
Location: Oklahoma City
Concentration: Life
Schools:Hard Knocks
 Q47  V42
Send PM
Re: crazy exponent problem [#permalink] New post   31 Jul 2008, 13:23
this one has been discussed quite frequently :-D
User avatar
spriya
Director
Director
Joined: 17 Jun 2008
Posts: 617
Own Kudos [?]: 2902 [0]
Given Kudos: 0
Send PM
Re: crazy exponent problem [#permalink] New post   03 Aug 2008, 06:14
imadummy wrote:
Hi All, would someone please help explain this question? It's from GMAP Prep 1. Many thanks.

5^21 * 4^11 = 2 * 10^N
N=?


its just simplifying the problm is what is important here :
5^21 * 4^11 = 5^21 * 2^22 = (10^21) *2 =2*10^N => N=21

n=21 is answer :)



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 above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: crazy exponent problem [#permalink]
03 Aug 2008, 06:14
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 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