Each of the following equations has at least one solution EXCEPT:
A. -2^n = (-2)^-n
B. 2^-n = (-2)^n
C. 2^n = (-2)^-n
D. (-2)^n = -2^n
E. (-2)^-n = -2^-n
For many test-takers, the most practical approach will be to eliminate the four answer choices that DO have at least one solution.
Values likely to work in a majority of the answer choices are n=0 and n=1.
Plug n=0 and n=1 into the answer choices:
A. -2^n = (-2)^-n
n=0:
-(2^0) = (-2)^-0
-1 = 1. Doesn't work.
n=1:
-(2^1) = (-2)^-1
-2 = -1/2. Doesn't work.
Hold onto A.
B. 2^-n = (-2)^n
n=0:
2^-0 = (-2)^0
1=1.
n=0 is a solution. Eliminate B.
C. 2^n = (-2)^-n
n=0:
2^0 = (-2)^-0
1=1.
n=0 is a solution. Eliminate C.
D. (-2)^n = -2^n
n=1:
(-2)^1 = -(2^1)
-2 = -2.
n=1 is a solution. Eliminate D.
E. (-2)^-n = -2^-n
n=1:
(-2)^(-1) = -(2^-1)
-1/2 = - 1/2
n=1 is a solution. Eliminate E.
The correct answer is
A.
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
