Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 28 May 2016, 18:13

### 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 n = 10^10 and n^n = 10^d, what is the value of d?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 38 [1] , given: 23

If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

### Show Tags

13 Sep 2013, 17:36
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

49% (01:39) correct 51% (01:10) wrong based on 281 sessions

### HideShow timer Statistics

If n = 10^10 and n^n = 10^d, what is the value of d?

A. 10^3
B. 10^10
C. 10^11
D. 10^20
E. 10^100

[Reveal] Spoiler:
I chose A and it was obviously incorrect but I can't figure out why. I thought that I could multiply exponents, doesn't that mean that I would essentially have, -(10^10)^(10^10) = 10^d
-10^10.10.10 = 10^d
-10^1000 = 10^d
d= 1,000 = 10^3?

Why doesn't that work?

Thanks!
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Sep 2013, 02:57, edited 3 times in total.
Edited the question.
Manager
Joined: 30 May 2013
Posts: 190
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 50 [0], given: 72

Re: If n = 10^10 and n^n = 10d, what is the value of d? [#permalink]

### Show Tags

13 Sep 2013, 20:47
russ9 wrote:
If n = 10^10 and n^n = 10d, what is the value of d?

10^3
10^10
10^11
10^20
10^100

I chose A and it was obviously incorrect but I can't figure out why. I thought that I could multiply exponents, doesn't that mean that I would essentially have, -(10^10)^(10^10) = 10^d
-10^10.10.10 = 10^d
-10^1000 = 10^d
d= 1,000 = 10^3?

Why doesn't that work?

Thanks!

Hi,

n^n=
=(10^10)^(10^10)
this can be written as
= 10^(10*10^10)
=10^(10^11)

Refer Gmat Math book:

math-number-theory-88376.html#p666609

Regards,
Rrsnathan
Intern
Joined: 14 Feb 2012
Posts: 29
Followers: 0

Kudos [?]: 5 [0], given: 6

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

### Show Tags

22 Oct 2013, 07:16
Can someone propose another approach?
Manager
Joined: 24 Apr 2013
Posts: 71
Location: United States
Followers: 0

Kudos [?]: 10 [0], given: 23

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

### Show Tags

22 Oct 2013, 09:58
1
This post was
BOOKMARKED
I know we should apply this rule:

$$(a^m)^n$$=$$a^{mn}$$

a$$^m^n$$=$$a^{(m^n)}$$and not $$(a^m)^n$$

but I still have a problem in applying it to this question
_________________

Struggling: make or break attempt

Math Expert
Joined: 02 Sep 2009
Posts: 33055
Followers: 5770

Kudos [?]: 70726 [3] , given: 9856

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

### Show Tags

22 Oct 2013, 10:23
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
SaraLotfy wrote:
I know we should apply this rule:

$$(a^m)^n$$=$$a^{mn}$$

a$$^m^n$$=$$a^{(m^n)}$$and not $$(a^m)^n$$

but I still have a problem in applying it to this question

If n = 10^10 and n^n = 10^d, what is the value of d?
A. 10^3
B. 10^10
C. 10^11
D. 10^20
E. 10^100

Since $$n = 10^{10}$$, then $$n^n=(10^{10})^{(10^{10})}=10^{10*10^{10}}=10^{10^{11}}$$.

$$10^{10^{11}}=10^d$$ --> $$d=10^{11}$$.

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 35

Kudos [?]: 1520 [1] , given: 193

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

### Show Tags

24 Feb 2014, 03:18
1
KUDOS
1
This post was
BOOKMARKED
Did in this way:

$$n = 10^{10}$$

$$(10^{10})^{(10^{10})} = 10^d$$ ........... As per equation

Can be re-written as

$$(10^{10})^{(10^{10})} = 10^{(d * 10 * \frac{1}{10})}$$

can be re-written as

$$(10^{10})^{(10^{10})} = (10^{10})^{(\frac{d}{10})}$$

Bases are same, so equating powers

$$\frac{d}{10} = 10^{10}$$

$$d = 10^{11} = Answer = C$$
_________________

Kindly press "+1 Kudos" to appreciate

Last edited by PareshGmat on 24 Apr 2014, 00:37, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6578
Location: Pune, India
Followers: 1794

Kudos [?]: 10786 [4] , given: 211

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

### Show Tags

24 Feb 2014, 22:40
4
KUDOS
Expert's post
SaraLotfy wrote:
I know we should apply this rule:

$$(a^m)^n$$=$$a^{mn}$$

a$$^m^n$$=$$a^{(m^n)}$$and not $$(a^m)^n$$

but I still have a problem in applying it to this question

Yes, I guess many people will have a similar feeling. Think of it not in terms of exponents but simple numbers.

Imagine what 10^10 is: n = 10000000000 (it has 10 zeroes)
$$n^n = 10000000000^{10000000000} = (10^{10})^{10000000000} = 10^{100000000000}$$ (now it has 11 zeroes)
$$10^d = 10^{100000000000}$$

So $$d = 100000000000 = 10^{11}$$
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9667
Followers: 465

Kudos [?]: 120 [0], given: 0

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

### Show Tags

30 Jun 2015, 09:32
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.
_________________
Manager
Joined: 28 Jun 2015
Posts: 139
Concentration: Finance, Economics
GPA: 3.5
Followers: 0

Kudos [?]: 48 [0], given: 19

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]

### Show Tags

30 Jun 2015, 10:25
n = 10^10
n^n = 10^d
now, n^n = 10^10^n = 10^10n.
so, 10^d = 10^10n
d = 10(10^10) = 10^11
_________________

I used to think the brain was the most important organ. Then I thought, look what’s telling me that.

Re: If n = 10^10 and n^n = 10^d, what is the value of d?   [#permalink] 30 Jun 2015, 10:25
Similar topics Replies Last post
Similar
Topics:
9 If n=10^{100} and n^{n}=10^{k}, what is the value of k? 4 19 Apr 2015, 10:42
1 If 1<=n<=99 and n is an integer, what is the probability that n(n + 1) 2 08 Feb 2015, 11:01
3 What is the value of n^2? 4 03 Dec 2013, 09:48
2 If A(n)=1/(n(n+1)) for all positive integers n, what is the 3 01 Sep 2013, 12:46
13 For which of the following values of n is (100+n)/n NOT an 12 23 Jul 2012, 04:19
Display posts from previous: Sort by