It is currently 25 Feb 2018, 15:42

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# 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

Manager
Joined: 03 Aug 2010
Posts: 104
GMAT Date: 08-08-2011
If 5^21 * 4^11 = 2 * 10^n, what is the value of n? [#permalink]

### Show Tags

08 Aug 2010, 20:12
1
KUDOS
15
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

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
[Reveal] Spoiler: OA

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
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

_________________

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
Expert's post
7
This post was
BOOKMARKED
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 --> $$n=21$$.

_________________
Manager
Joined: 03 Aug 2010
Posts: 104
GMAT Date: 08-08-2011
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
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
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
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
GMAT 1: 700 Q50 V34
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
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/vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

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
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
_________________

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
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
2
KUDOS
Expert's post
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/absolute-modulus-a-better-understanding-210849.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

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study 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
Display posts from previous: Sort by

# 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 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®.