Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jul 1311:00 AM EDT
-12:30 PM EDT
Looking for your GMAT motivation to break through the score plateau? Pragati improved her score by massive 160 points with strategic guidance and hard-work! Find out how personalized mentorship and a strong mindset can turn GMAT struggles into success.
Jul 0901:00 PM EDT
-02:00 PM EDT
More Target Test Prep students are earning 100th percentile GMAT scores. Don’t settle for less when the Target Test Prep course gives you everything you need to score high on the GMAT. Start your 5-day free trial today.
Jul 1206:30 AM PDT
-08:30 AM PDT
Join our webinar to master GMAT RC Main Point Questions! Learn effective strategies to decipher passage themes and purposes. Senior Verbal Expert- Sunita Singhvi will equip you with tools to navigate complexities and avoid common traps set by the GMAT.
Jul 1508:00 PM PDT
-09:00 PM PDT
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Jul 1611:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
Jul 1911:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment
29 Sep 2010, 06:13
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:22) correct
33%
(01:10)
wrong
based on 3513
sessions
History
Date
Time
Result
Not Attempted Yet
For how many integers n is 2^n = n^2 ?
A. None
B. One
C. Two
D. Three
E. More than Three
A. None
B. One
C. Two
D. Three
E. More than Three
29 Sep 2010, 06:21
Kudos
Bookmarks
For how many integers n is 2^n = n^2 ?
A. None
B. One
C. Two
D. Three
E. More than Three
\(2^n= n^2\) is true for 2 integers:
\(n=2\) --> \(2^2=2^2=4\);
\(n=4\) --> \(4^2=2^4=16\).
Well, \(2^2=2^2=4\) is obvious choices, then after trial and error you'll get \(4^2=2^4=16\) as well. But how do we know that there are no more such numbers? You can notice that when \(n\) is more than 4 then \(2^n\) is always more than \(n^2\) so \(n\) cannot be more than 4. \(n\) cannot be negative either as in this case \(2^n\) won't be an integer whereas \(n^2\) will be.
Answer: C.
NOTE: I think it's worth remembering that \(4^2=16=2^4\), I've seen several GMAT questions on number properties using this (another useful property \(8^2=4^3=2^6=64\)).
Hope it helps.
A. None
B. One
C. Two
D. Three
E. More than Three
\(2^n= n^2\) is true for 2 integers:
\(n=2\) --> \(2^2=2^2=4\);
\(n=4\) --> \(4^2=2^4=16\).
Well, \(2^2=2^2=4\) is obvious choices, then after trial and error you'll get \(4^2=2^4=16\) as well. But how do we know that there are no more such numbers? You can notice that when \(n\) is more than 4 then \(2^n\) is always more than \(n^2\) so \(n\) cannot be more than 4. \(n\) cannot be negative either as in this case \(2^n\) won't be an integer whereas \(n^2\) will be.
Answer: C.
NOTE: I think it's worth remembering that \(4^2=16=2^4\), I've seen several GMAT questions on number properties using this (another useful property \(8^2=4^3=2^6=64\)).
Hope it helps.
General Discussion
29 Sep 2010, 08:03
Kudos
Bookmarks
vanidhar
for how many integers n is 2^n= n^2 ?
0
1
2
3
>3
0
1
2
3
>3
It helps to know that the function 2^x is more expansive than x^2 for large positive x and converges quickly to 0 for negative x.
So we know we only have to check small values of x. For positive x, it is easy to see this is true for x=2,4 and then the function 2^x explodes
For negative x, 2^-1 is less than -1^2 already so no negative integers can satisfy the equality
Answer is (c) or 2
