Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 16:23

### 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

# Events & Promotions

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

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 21 Aug 2008
Posts: 24
Followers: 0

Kudos [?]: 19 [0], given: 0

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

### Show Tags

03 Dec 2008, 14:24
00:00

Difficulty:

(N/A)

Question Stats:

63% (01:42) correct 38% (00:01) wrong based on 10 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
Director
Joined: 12 Jul 2008
Posts: 518
Schools: Wharton
Followers: 22

Kudos [?]: 155 [0], given: 0

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

### Show Tags

03 Dec 2008, 14:49
samlosco 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

B

5^21 * 4^11
= 5^21 * (2*2)^11
= 5^21 * 2^11 * 2^11
= 5^21 * 2^22
= 5^21 * 2^21 * 2
= 2 * 10^21
SVP
Joined: 30 Apr 2008
Posts: 1874
Location: Oklahoma City
Schools: Hard Knocks
Followers: 42

Kudos [?]: 590 [2] , given: 32

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

### Show Tags

03 Dec 2008, 14:59
2
KUDOS
I agree the answer is B.

This is no different than what zoinnk did. I'm just explaning the steps taken and rules that allow us to get to the answer.

It may help someone to break down these exponents for better understanding.

If you have $$4^{11}$$

That's the same thing as
4*4*4*4*4*4*4*4*4*4*4

Break down the 4's into 2's

(2*2)*(2*2)*(2*2)*(2*2)*(2*2)*(2*2)*(2*2)*(2*2)*(2*2)*(2*2)*(2*2)

Now count the 2's. There are 22, so $$4^{11} = 2^{22}$$

RULE: When multiplying numbers with exponents the base numbers (2 is the base of 2^3) can be multiplied if the exponent number is the same. Here we have 5^21 and 2^22. We can pull out a 2 from 2^22 to give us 2^21 * 2 * 5^21. Now we have similar exponent: 21. 5x2 = 10, so we have 2 * 10^21. When you multiply the bases the exponent must be the same, so the exponent remains the same when finished, hence $$5^{21}*2^{21} = 10^{21}$$ We pulled out a 2 in order to make the exponent 21 rather than 22 so we have:

2 * 10^21 which makes the value of n = 21.

samlosco 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

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a.

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Joined: 30 Nov 2008
Posts: 489
Schools: Fuqua
Followers: 10

Kudos [?]: 290 [0], given: 15

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

### Show Tags

04 Dec 2008, 10:48
Answer is B. Here is the approach

5^21 * 4^11 = 2 * 10^n
(5^11*5^10) * (2^11*2^10*2) = 2 * 10^n (Rule is = a ^ (m+n) = a ^ m * a * n )
10^11*10^10* 2 = 2 * 10^n (Multiple the base terms with same powers. a^m * b^ m = ab ^ m)
10^21*2 = 2*10^n

n = 21
Manager
Joined: 01 Mar 2009
Posts: 51
Followers: 1

Kudos [?]: 9 [0], given: 2

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

### Show Tags

28 Apr 2009, 10:34
If $$5^{21}*4^{11} = 2*10^n$$ what is the value of n?

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

I know I am suppose to work out the equation to get the integers to equal each other but just can't grasp it.

Thanks!
Director
Joined: 27 Jun 2008
Posts: 543
WE 1: Investment Banking - 6yrs
Followers: 2

Kudos [?]: 64 [1] , given: 92

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

### Show Tags

28 Apr 2009, 11:01
1
KUDOS
zalan 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

I know I am suppose to work out the equation to get the integers to equal each other but just can't grasp it.

Thanks!

> 5^21 * (2^2)*11 = 2 * 10^n
> 5^21 * 2^22 = 2 * (2^n*5^n)
> 5^21 * 2^22 = 2^n+1 * 5^n

i.e 5^21 = 5^n
n = 21

>2^22 = 2^n+1
>n+1 = 22.
>n=21

B
Director
Joined: 23 May 2008
Posts: 818
Followers: 3

Kudos [?]: 73 [0], given: 0

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

### Show Tags

29 Apr 2009, 09:41
5^21 * 4^11 = 2 * 10^n

5^21 * 2^22 = 2 * 10^n

5^21 * 2^21= 10^n

10^21 = 10^n

n=21
Current Student
Joined: 20 Jun 2009
Posts: 169
Schools: Yale SOM Class of 2013
Followers: 3

Kudos [?]: 36 [0], given: 0

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

### Show Tags

13 Feb 2010, 10:52
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

Clear, concise explanations welcome!

[Reveal] Spoiler:
OA = B
Senior Manager
Joined: 01 Feb 2010
Posts: 264
Followers: 1

Kudos [?]: 58 [0], given: 2

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

### Show Tags

13 Feb 2010, 10:57
carriedinterest 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

Clear, concise explanations welcome!

[Reveal] Spoiler:
OA = B

5^21 * 4^11 = 5^21 * 2^22 = 2 * (5*2)^21 = 2 * 10^21
hence B.
Manager
Status: Getting ready for the internship summer
Joined: 07 Jun 2009
Posts: 51
Location: Rochester, NY
Schools: Simon
WE 1: JPM - Treasury
Followers: 0

Kudos [?]: 28 [0], given: 23

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

### Show Tags

13 Feb 2010, 11:10
Break down the exponents on each side and the answer reveals itself:

$$5^{21} * 4^{11} = 2 * 10^n$$

Left side: $$4^{11} = (2 * 2)^{11} = 2^{22}$$

Right side: $$2 * 10^n = 2 * (5 * 2)^n = 2 * 5^n * 2^n$$

$$2^n * 2 = 2^{n+1}$$

Back together: $$5^{21} * 2^{22} = 5^n * 2^{n + 1}$$

$$n = 21$$
Senior Manager
Joined: 22 Dec 2009
Posts: 359
Followers: 11

Kudos [?]: 389 [0], given: 47

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

### Show Tags

13 Feb 2010, 11:13
carriedinterest 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

Clear, concise explanations welcome!

5^21 x 4^11 = 2 x 10^n
5^21 x 2^22 = 2 x 10^n
(5 x 2)^21 x 2 = 2 x 10^n
10^21 x 2 = 2 x 10^n

Therefore n = 21

B
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1180
Followers: 438

Kudos [?]: 1606 [0], given: 4

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

### Show Tags

13 Feb 2010, 19:57
carriedinterest 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

Clear, concise explanations welcome!

[Reveal] Spoiler:
OA = B

carriedinterest, I've seen this a few times - in the middle of a thread, you reprint the question from the first post, asking for 'clear, concise explanations' when there are already one or explanations that have already been provided - perhaps you did not find them clear or concise? In any case, I'm curious why you've done this; you did the same in these threads, for example:

gmatclub.com/forum/exponent-question-90368.html
gmatclub.com/forum/gmat-prep-1-symbolism-90366.html

If there is something in the solutions already given that is unclear to you, then it would be more helpful to point that out; surely other test takers share your concerns, and you can all benefit from having that detail of the solution explained. Or, if you are asking if there are alternative solution methods, it would be good to mention that. Otherwise, as has happened in each of these threads, people simply end up typing up the same solutions that were posted above, and I don't know that that benefits anyone much.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Math Expert
Joined: 02 Sep 2009
Posts: 38908
Followers: 7739

Kudos [?]: 106246 [0], given: 11618

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

### Show Tags

14 Feb 2010, 03:22
IanStewart wrote:
carriedinterest 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

Clear, concise explanations welcome!

[Reveal] Spoiler:
OA = B

carriedinterest, I've seen this a few times - in the middle of a thread, you reprint the question from the first post, asking for 'clear, concise explanations' when there are already one or explanations that have already been provided - perhaps you did not find them clear or concise? In any case, I'm curious why you've done this; you did the same in these threads, for example:

gmatclub.com/forum/exponent-question-90368.html
gmatclub.com/forum/gmat-prep-1-symbolism-90366.html

If there is something in the solutions already given that is unclear to you, then it would be more helpful to point that out; surely other test takers share your concerns, and you can all benefit from having that detail of the solution explained. Or, if you are asking if there are alternative solution methods, it would be good to mention that. Otherwise, as has happened in each of these threads, people simply end up typing up the same solutions that were posted above, and I don't know that that benefits anyone much.

Ian, It was I, who merged the topics as carriedinterest posted several question that were already discussed. Guess I should mentioned this in the thread after doing so. Sorry for confusion.
_________________
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1180
Followers: 438

Kudos [?]: 1606 [0], given: 4

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

### Show Tags

14 Feb 2010, 04:26
Ah, I see - my apologies! It did seem very odd, so I was curious to know why it was happening, but that makes a lot of sense.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2013
Followers: 163

Kudos [?]: 1826 [0], given: 376

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

### Show Tags

05 Feb 2011, 22:40
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"
_________________
Re: If 5^21*4^11 = 2*10^n, what is the value of n?   [#permalink] 05 Feb 2011, 22:40
Similar topics Replies Last post
Similar
Topics:
5 If 3^(2n) = (1/9)^(n+2), what is the value of n? 3 22 Mar 2016, 15:15
What is the value of N such that 3 06 May 2015, 23:53
16 If n=10^{100} and n^{n}=10^{k}, what is the value of k? 5 27 Oct 2016, 18:57
17 What is the value of n if the sum of the consecutive odd 6 26 Oct 2016, 12:03
28 If n = 10^10 and n^n = 10^d, what is the value of d? 9 12 Jul 2016, 19:01
Display posts from previous: Sort by