GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 02 Jun 2020, 11:00

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.

Close

Request Expert Reply

Confirm Cancel

If 5^21 * 4^11 = 2 * 10^n, what is the value of n?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 03 Aug 2010
Posts: 80
GMAT Date: 08-08-2011
If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post Updated on: 04 Oct 2017, 05:39
5
23
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (01:02) correct 14% (01:39) wrong based on 550 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

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
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64174
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 09 Aug 2010, 02:36
4
1
8
Yalephd wrote:
If 5^21 X 4^11 = 2x10^n. What is the value of n?

A. 11
B. 21
C. 22
D. 23
E. 32


When we have exponents on both sides it's good idea to get common base.

We have \(5^{21}*4^{11}=2*10^n\). Little trick for this question: we can forget about 2's on both sides and concentrate on 5-s --> \(5^{21}*4^{11}=2*2^n*5^n\) --> powers of 5 on both sides must be equal --> \(n=21\).

Answer: B.
_________________
Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 311
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

New post 08 Aug 2010, 20:41
5
6
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)
General Discussion
Manager
Manager
avatar
Joined: 03 Aug 2010
Posts: 80
GMAT Date: 08-08-2011
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 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
Manager
avatar
Joined: 16 Apr 2010
Posts: 168
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 09 Aug 2010, 05:15
1
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
Senior Manager
User avatar
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 311
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

New post 14 Aug 2010, 15:12
1
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.
Director
Director
avatar
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 571
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

New post 23 Aug 2010, 08:36
1
1
5^21 2^22 = 2 10^n
10^21 = 10^n
Hence n = 21

Posted from my mobile device
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1469
Re: If 5^21*4^11 = 2*10^n, what is the value of n?  [#permalink]

Show Tags

New post 05 Feb 2011, 21:40
2
These types are usually solved by reducing the term to prime factors and few common rules of exponent.

5^21 * 4^11 = 2 * 10^n

Consider the bases first; 5,4,2,10
5 and 2 are already primes; 4 and 10 composites.
Reduce these to prime factors:
4=2*2
10=5*2
Place in the equation:

\(5^{21} * 4^{11} = 2 * 10^n\)
\(5^{21} * (2*2)^{11} = 2 * (2*5)^n\)
\(5^{21} * (2)^{11} *(2)^{11}= 2 * (2)^n*(5)^n\)
##\((x*y)^m = x^m * y^m\)#### Rule of exponent##
\(5^{21} * (2)^{22} = (5)^n * 2^{(n+1)}\)
##\(x^m*x^n = x^{(m+n)}\)## Rule of exponent##

Compare LHS and RHS
n+1=22
n=21

Ans: "B"
Director
Director
User avatar
Joined: 14 Dec 2012
Posts: 670
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
GMAT ToolKit User
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post Updated on: 04 Aug 2013, 10:36
2
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/vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment
: 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
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 427
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 04 Aug 2013, 10:36
4
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
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1707
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

New post Updated on: 15 Apr 2014, 00:56
4
\(5^{21} * 4^{11} = 2*10^p\)

\(5^{21} * 2^{22} = 2*10^p\)

\(2 * 2^{21} * 5^{21} = 2*10^p\)

\(2 * 10^{21} = 2*10^p\)

Equating powers, p = 21 = Answer B

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
User avatar
V
Joined: 16 Oct 2010
Posts: 10490
Location: Pune, India
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 14 Apr 2014, 17:23
2
1
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 >
Board of Directors
User avatar
V
Status: Emory Goizueta Alum
Joined: 18 Jul 2015
Posts: 3585
Reviews Badge CAT Tests
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 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 LinkedIn abhimahna. | 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
GMAT Club Inbuilt Error Log Functionality - View More | Best Reply Functionality on GMAT Club!
New Visa Forum - Ask all your Visa Related Questions - here | Have OPT questions? - Post them here.
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. | Blog: Subscribe to Question of the Day Blog
New! Executive Assessment (EA) Exam - All you need to know!
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8626
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 28 Aug 2016, 05:38
1
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
_________________
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10645
Location: United States (CA)
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 06 Oct 2017, 09:53
1
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 Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
B
Joined: 03 Oct 2016
Posts: 37
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 14 Feb 2020, 09:32
ScottTargetTestPrep wrote:
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


Hi Scott,

i like the way you solved the above problem. Just a small question.
In the above simplification, did you divide 2^22 by 2^1(on the left hand side) to make it 2^21?
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10645
Location: United States (CA)
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

New post 16 Feb 2020, 17:44
2
kanak2016 wrote:
ScottTargetTestPrep wrote:
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


Hi Scott,

i like the way you solved the above problem. Just a small question.
In the above simplification, did you divide 2^22 by 2^1(on the left hand side) to make it 2^21?


That's exactly what I did. I divided each side by 2^1 so that we are left with 10^n on one side and subtracted the exponents of 2 on the other side to obtain 2^{22 - 1} = 2^21.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?   [#permalink] 16 Feb 2020, 17:44

If 5^21 * 4^11 = 2 * 10^n, what is the value of n?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne