GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If n = 10^10 and n^n = 10^d, what is the value of d?
[#permalink]
22 Feb 2021, 09:53
22 Feb 2021, 09:53
1
Expert Reply
5
Bookmarks
00:00
Question Stats:
54% (01:10) correct
45% (01:32) wrong based on 83 sessions
Hide Show 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. \(10^{100}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
If n = 10^10 and n^n = 10^d, what is the value of d?
[#permalink]
22 Feb 2021, 10:13
22 Feb 2021, 10:13
3
1
Bookmarks
Carcass wrote:
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. \(10^{100}\)
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
Good Question Carcass
\(n^n = 10^d\)
\((10^{10})^n = 10^d\) ...................... [Since, \(n = 10^{10}\)]
\(10^{10n} = 10^d\)
When the bases are equal, powers are equal
\(10n = d\)
\((10)(10)^{10} = d\)
\(10^{1+10} = d\)
\(10^{11} = d\)
Hence, option C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If n = 10^10 and n^n = 10^d, what is the value of d?
[#permalink]
22 Feb 2021, 10:25
22 Feb 2021, 10:25
1
Carcass wrote:
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. \(10^{100}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. \(10^3\)
B. \(10^{10}\)
C. \(10^{11}\)
D. \(10^{20}\)
E. \(10^{100}\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Key property: \((b^x)^y = b^{xy}\)
If \(n = 10^{10}\), then \(n^n = (10^{10})^{(10^{10})} = 10^d\)
At this point, it helps to compare \((10^{10})^{(10^{10})}\) with \((b^x)^y\)
We can see that \(b \) \( = 10\), \(x \) \( = 10\) and \(y \) \( = 10^{10}\)
This means \(xy\) \(= (10)(10^{10})=(10^1)(10^{10})= 10^{11}\)
In other words: \((10^{10})^{(10^{10})} = 10^{(10^{11})} = 10^d\)
So, \(d=10^{11}\)
Answer: C
RELATED VIDEO
