GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 05:23 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  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: 84
GMAT Date: 08-08-2011
If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

5
22 00:00

Difficulty:   5% (low)

Question Stats: 85% (01:02) correct 15% (01:38) wrong based on 801 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, 21:12.
Last edited by Bunuel on 04 Oct 2017, 06:39, edited 4 times in total.
Edited the question
Math Expert V
Joined: 02 Sep 2009
Posts: 58449
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

4
1
7
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 --> $$n=21$$.

_________________
Senior Manager  Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 328
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

5
5
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 General Discussion
Manager  Joined: 03 Aug 2010
Posts: 84
GMAT Date: 08-08-2011
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

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: 180
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

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  Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 328
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

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.
_________________ Support GMAT Club by putting a GMAT Club badge on your blog Director  Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 583
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

1
1
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
Retired Moderator Joined: 20 Dec 2010
Posts: 1578
Re: If 5^21*4^11 = 2*10^n, what is the value of n?  [#permalink]

Show Tags

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  Joined: 14 Dec 2012
Posts: 703
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

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

Originally posted by blueseas on 04 Aug 2013, 11:31.
Last edited by blueseas on 04 Aug 2013, 11:36, edited 1 time in total.
Senior Manager  B
Joined: 24 Aug 2009
Posts: 445
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

3
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: 1749
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

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
_________________
Kindly press "+1 Kudos" to appreciate Originally posted by PareshGmat on 26 Feb 2014, 21:58.
Last edited by PareshGmat on 15 Apr 2014, 01:56, edited 1 time in total.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

2
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 V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3580
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

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

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 V
Joined: 02 Aug 2009
Posts: 7984
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

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 D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?  [#permalink]

Show Tags

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

Scott@TargetTestPrep.com

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.

Non-Human User Joined: 09 Sep 2013
Posts: 13271
Re: Exponent Problem (simple)  [#permalink]

Show Tags

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.
_________________ Re: Exponent Problem (simple)   [#permalink] 11 Oct 2019, 04:40
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  