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

 It is currently 23 May 2015, 19:57

### 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:
Senior Manager
Joined: 15 Aug 2013
Posts: 331
Followers: 0

Kudos [?]: 21 [1] , given: 23

If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]  13 Sep 2013, 16:36
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

44% (01:38) correct 56% (01:21) wrong based on 178 sessions
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, 01:57, edited 3 times in total.
Edited the question.
Manager
Joined: 30 May 2013
Posts: 193
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 32 [0], given: 72

Re: If n = 10^10 and n^n = 10d, what is the value of d? [#permalink]  13 Sep 2013, 19:47
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: 30
Followers: 0

Kudos [?]: 4 [0], given: 6

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]  22 Oct 2013, 06:16
Can someone propose another approach?
Manager
Joined: 24 Apr 2013
Posts: 75
Location: United States
Followers: 0

Kudos [?]: 8 [0], given: 23

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]  22 Oct 2013, 08:58
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: 27468
Followers: 4311

Kudos [?]: 42184 [2] , given: 5957

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]  22 Oct 2013, 09:23
2
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

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: 22

Kudos [?]: 895 [1] , given: 193

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]  24 Feb 2014, 02:18
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 23 Apr 2014, 23:37, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5539
Location: Pune, India
Followers: 1368

Kudos [?]: 6964 [3] , given: 178

Re: If n = 10^10 and n^n = 10^d, what is the value of d? [#permalink]  24 Feb 2014, 21:40
3
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

Re: If n = 10^10 and n^n = 10^d, what is the value of d?   [#permalink] 24 Feb 2014, 21:40
Similar topics Replies Last post
Similar
Topics:
3 For all integers n, n* = n(n – 1). what is the value of x* 3 14 Jul 2013, 19:34
What is the value of the integer n? (1) n(n + 2) = 15 (2) 3 22 Aug 2009, 10:03
For all nonzero integers, n*=(N+2)/N. What is the value of 3 25 Nov 2007, 03:09
What is the value of the integer n 1. n(n+2)=15 2. 4 14 Jun 2006, 19:11
The function n* can be written as n(n-1). What is the value 3 29 May 2006, 04:24
Display posts from previous: Sort by

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.