Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 03 Aug 2010
Posts: 104
GMAT Date: 08082011

If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]
Show Tags
08 Aug 2010, 20:12
1
This post received KUDOS
15
This post was BOOKMARKED
Question Stats:
85% (00:36) correct 15% (00:49) wrong based on 537 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.
Last edited by Bunuel on 04 Oct 2017, 05:39, edited 4 times in total.
Edited the question



Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 403
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
4
This post received KUDOS
5
This post was BOOKMARKED
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



Math Expert
Joined: 02 Sep 2009
Posts: 43917

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



Manager
Joined: 03 Aug 2010
Posts: 104
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: 211

Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]
Show Tags
09 Aug 2010, 05:15
1
This post received KUDOS
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: 403
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
1
This post received KUDOS
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: 23

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: 674
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
1
This post received KUDOS
1
This post was BOOKMARKED
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: 403
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: 212

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: 832
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
04 Aug 2013, 10:31
1
This post received KUDOS
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
Last edited by blueseas on 04 Aug 2013, 10:36, edited 1 time in total.



Senior Manager
Joined: 24 Aug 2009
Posts: 489
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
3
This post received KUDOS
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: 1839
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
26 Feb 2014, 20:58
3
This post received KUDOS
\(5^{21} * 4^{11} = 2*10^p\) \(5^{21} * 2^{22} = 2*10^p\) \(2 * 2^{21} * 5^{21} = 2*10^p\) \(2 * 10^{21} = 2*10^p\) Equating powers, p = 21 = Answer B
_________________
Kindly press "+1 Kudos" to appreciate
Last edited by PareshGmat on 15 Apr 2014, 00:56, edited 1 time in total.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7960
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 My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3092

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
_________________
How I improved from V21 to V40! ? How to use this forum in THE BEST way?



Math Expert
Joined: 02 Aug 2009
Posts: 5663

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
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
BANGALORE/



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
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




Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
[#permalink]
06 Oct 2017, 09:53






