For how many integers n is 2^n = n^2
a. none
b. one
c. two
d. three
e. more than 3
this seemed like such an easy question. i plugged in 1 found it was not one of the integers, plugged in -1 and it also was not one of them. Plugged in 0 and that did not work. Figured it was NONE
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
Integer N
This topic has expert replies
-
neelgandham
- Community Manager
- Posts: 1060
- Joined: Fri May 13, 2011 6:46 am
- Location: Utrecht, The Netherlands
- Thanked: 318 times
- Followed by:52 members
2^2 = 2^2fangtray wrote:For how many integers n is 2^n = n^2
a. none
b. one
c. two
d. three
e. more than 3
2^4 = 4^2, So the answer should be [spoiler]C = 2[/spoiler]
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
We can solve this problem by trial and error method.
We will plug in values for n from 1,2,3,.... and chk for which value of n, 2^n = n^2.
1)n=1
2 = 1 FALSE
2)n=2
2^2 = 4; n^2 = 4 TRUE
3) n =3
2^3 = 8; 3^2 = 9 FALSE
4) n=4
2^4 = 16; 4^2=16 TRUE
5)n=5
2^5=32; 5^2=25 FALSE
6) n=6
2^6=64; 6^2 =36 FALSE
From this we can say that, as n increases, 2^n >> n^2.
hence for 2 values of n, this will hold true. SO the answer is option C
We will plug in values for n from 1,2,3,.... and chk for which value of n, 2^n = n^2.
1)n=1
2 = 1 FALSE
2)n=2
2^2 = 4; n^2 = 4 TRUE
3) n =3
2^3 = 8; 3^2 = 9 FALSE
4) n=4
2^4 = 16; 4^2=16 TRUE
5)n=5
2^5=32; 5^2=25 FALSE
6) n=6
2^6=64; 6^2 =36 FALSE
From this we can say that, as n increases, 2^n >> n^2.
hence for 2 values of n, this will hold true. SO the answer is option C
-
Birottam Dutta
- Master | Next Rank: 500 Posts
- Posts: 342
- Joined: Wed Jul 08, 2009 8:50 am
- Thanked: 214 times
- Followed by:19 members
- GMAT Score:740
In addition to the answers above, you may also draw a graph of the two functions 2^N and N^2 and see where they intersect. There will be two points which gives the answer to the question.
Hence, answer C.
Hence, answer C.
-
ronnie1985
- Legendary Member
- Posts: 626
- Joined: Fri Dec 23, 2011 2:50 am
- Location: Ahmedabad
- Thanked: 31 times
- Followed by:10 members
