November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 23, 2018 November 23, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 03 Aug 2010
Posts: 98
GMAT Date: 08082011

If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
Updated on: 04 Oct 2017, 05:39
Question Stats:
85% (00:35) correct 15% (00:43) wrong based on 656 sessions
HideShow timer Statistics
If \(5^{21} * 4^{11} = 2 * 10^n\), what is the value of n? A. 11 B. 21 C. 22 D. 23 E. 32
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Yalephd on 08 Aug 2010, 20:12.
Last edited by Bunuel on 04 Oct 2017, 05:39, edited 4 times in total.
Edited the question




Math Expert
Joined: 02 Sep 2009
Posts: 50728

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
09 Aug 2010, 02:36




Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 365
Location: Milky way
Schools: ISB, Tepper  CMU, Chicago Booth, LSB

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
08 Aug 2010, 20:41
My attempt: 5^(21) * 4^(11) = 2*10^p 5^(21) * 2 ^ (22) = 2 * (2*5)^p 5^(21) * 2 ^ (22) = 2 * 2^(p) * 5^(p) 5^(21) * 2 ^ (22) = 2^(p+1) * 5^(p) => (p+1) = 22 => p = 21 Answer: 21 (B)
_________________
Support GMAT Club by putting a GMAT Club badge on your blog




Manager
Joined: 03 Aug 2010
Posts: 98
GMAT Date: 08082011

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
09 Aug 2010, 03:57
I got it now using ezhilkumarank's method. Thanks. Bunuel, I don't follow your method. Are you saying that 5^21 * 4^11 = 2 * 2^21 * 5^21



Manager
Joined: 16 Apr 2010
Posts: 200

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
09 Aug 2010, 05:15
Yalephd,
What Bunuel is trying to say is that save time by considering only 5
We have 10^p = (2*5)^p = 2^p * 5^p



Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 365
Location: Milky way
Schools: ISB, Tepper  CMU, Chicago Booth, LSB

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
14 Aug 2010, 15:12
vasili wrote: Can somebody please put detailed explanation? Thanks.
If 5^21 x 4^11=2x10^n, what's n?
11 21 22 23 32 @ vasili  This question is already answered in one of the earlier post. Kindly search for the question once before posting. 5^21 * 4^11=2*10^n = 5^21 * 4^11=2*(2*5)^n = 5^21 * 4^11 = 2^(n+1) * 5^n => n = 21.
_________________
Support GMAT Club by putting a GMAT Club badge on your blog



Intern
Joined: 26 May 2010
Posts: 22

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
23 Aug 2010, 08:27
I know there is an easy way to solve this quickly, but I am wondering if someone can explain it:
5^21 x 4 ^11 = 2 x 10 ^ n
What is n?
Thank you very much.



Director
Status: Apply  Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 626
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
23 Aug 2010, 08:36
5^21 2^22 = 2 10^n 10^21 = 10^n Hence n = 21 Posted from my mobile device
_________________
Consider kudos, they are good for health



Intern
Joined: 22 Jun 2010
Posts: 3

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
26 Aug 2010, 18:08
I have a weird mind block around this question.... what is the value of n if, 5^21 x 4^11 = 2 x 10^n Ugh, it seems like it should be so easy! what am I not getting? Thanks so much in advance for anyone who can shine some light onto this!



Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 365
Location: Milky way
Schools: ISB, Tepper  CMU, Chicago Booth, LSB

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
26 Aug 2010, 18:10
kaptnmorgz wrote: I have a weird mind block around this question.... what is the value of n if, 5^21 x 4^11 = 2 x 10^n Ugh, it seems like it should be so easy! what am I not getting? Thanks so much in advance for anyone who can shine some light onto this! This is easy. Just try to isolate the powers of the distinct primes and then solve for x. P.S: This question is already discussed earlier. You may search for the answer once after trying again.
_________________
Support GMAT Club by putting a GMAT Club badge on your blog



Manager
Joined: 24 Dec 2009
Posts: 183

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
26 Aug 2010, 22:07
simplification is 
5^21 * 2^22 = 2 * 2^n * 5^n = 2^(n+1) * 5^n
comparing L.H.S and R.H.S, n = 21
Thanks.



Director
Joined: 14 Dec 2012
Posts: 766
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
Updated on: 04 Aug 2013, 10:36
njkhokh wrote: If 5^21 x 4^11 = 2 x 10^n what is the value of n?
A) 11 B) 21 C) 22 D) 23 E) 32 \(5^21\)\(*4^11\) \(= 2*10^n\) \(5^21* 2^22 = 2 *10^n\) ( AS \(4^11= (2^2)^11\)) \((5.2)^21 * 2 = 2 * 10^n\) HENCE n = 21
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
GIVE VALUE TO OFFICIAL QUESTIONS...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss
Originally posted by blueseas on 04 Aug 2013, 10:31.
Last edited by blueseas on 04 Aug 2013, 10:36, edited 1 time in total.



Senior Manager
Joined: 24 Aug 2009
Posts: 472
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
04 Aug 2013, 10:36
njkhokh wrote: If 5^21 x 4^11 = 2 x 10^n what is the value of n? A) 11 B) 21 C) 22 D) 23 E) 32 5^21 x 4^11 = 2 x 10^n 5^21 x 2^22 = 2 x 10^n 2 x 5^21 x 2^21 = 2 x 10^n 2 x 10^21 = 2 x 10^n Thus n = 21 Answer B
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1826
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
Updated on: 15 Apr 2014, 00:56
\(5^{21} * 4^{11} = 2*10^p\) \(5^{21} * 2^{22} = 2*10^p\) \(2 * 2^{21} * 5^{21} = 2*10^p\) \(2 * 10^{21} = 2*10^p\) Equating powers, p = 21 = Answer B
_________________
Kindly press "+1 Kudos" to appreciate
Originally posted by PareshGmat on 26 Feb 2014, 20:58.
Last edited by PareshGmat on 15 Apr 2014, 00:56, edited 1 time in total.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8578
Location: Pune, India

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
14 Apr 2014, 17:23
ausadj18 wrote: hi, all!
quick exponent question which seems easy but i cant seem to get my head around it  reallly appreciate your help!!
If 5^21 x 4^11 = 2 x 10^n,, what is value of n?
answer is 21, but honestly cant remember quite how to get here  thanks again for any help! Thumb rule for any exponents question: Deal only in prime numbers. \(5^{21} * 4^{11} = 2 * 10^n\) \(5^{21} * 2^{22} = 2 * 2^n * 5^n\) \(5^{21} * 2^{22} = 2^{n+1} * 5^n\) Now match the exponents of same prime numbers. Power of 5 on both sides should be equal. 21 = n or Power of 2 on both sides should be equal. 22 = n+1 n = 21
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3615

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
27 Aug 2016, 22:53
SharmaShruti wrote: 5^21 X 4^11 = 2 X 10^n. What is the value of n? a) 11 b) 21 c) 22 d) 23 e)32 The given expression \(5^21 * 4^(11) = 2 * 10^n\) can be written as \(5^21 * 2^22 = 2 * 5^n * 2^n\) or \(5^21 * 2^22 = 5^n * 2^(n+1)\) Comparing the powers of 2 on both sides, we will have \(2^22 = * 2^(n+1)\) or 22=n+1 or n=21. hence B
_________________
My GMAT Story: From V21 to V40 My MBA Journey: My 10 years long MBA Dream My Secret Hacks: Best way to use GMATClub  Importance of an Error Log! Verbal Resources: All SC Resources at one place  All CR Resources at one place Blog: Subscribe to Question of the Day Blog GMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here. New! Best Reply Functionality on GMAT Club! Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free Check our new About Us Page here.



Math Expert
Joined: 02 Aug 2009
Posts: 7044

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
28 Aug 2016, 05:38
SharmaShruti wrote: 5^21 X 4^11 = 2 X 10^n. What is the value of n? a) 11 b) 21 c) 22 d) 23 e)32 Hi, One does not require to simplify anything.. On left hand side, the power of 5 is 21..... But on right side it is part of 10.. so power of 10 has to be same as that of 5.. Ans 21
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
06 Oct 2017, 09:53
Yalephd 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 We can simplify the given equation: 5^21 x 2^22 = 2^1 x 10^n 5^21 x 2^21 = 10^n 10^21 = 10^n 21 = n Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



NonHuman User
Joined: 09 Sep 2013
Posts: 8870

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
Show Tags
28 Oct 2018, 16:38
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? &nbs
[#permalink]
28 Oct 2018, 16:38






