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by j_shreyans » Mon Oct 06, 2014 9:01 am
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

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by Brent@GMATPrepNow » Mon Oct 06, 2014 9:06 am
j_shreyans wrote: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

OAA
The notation here is ambiguous.
For the left side of equation A, is it -(2^n) or (-2)^n?
Likewise, for the right side of D, is it (2^n) or (-2)^n?

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by Brent@GMATPrepNow » Mon Oct 06, 2014 9:12 am
j_shreyans wrote: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)

OAA
I added some brackets to show, what I believe to be, the intent of the question.

Scanning the answer choices, it seems that n = 1 or n = 0 are possible solutions for each equation.
So, I might start TESTING each possible value of n for each option.

A) -(2^n) = (-2)^-n
n = 0 doesn't work
n = 1 doesn't work
So, keep A for now

B) 2^(-n) = (-2)^n
n = 0 works, We get: 1 = 1
ELIMINATE B

C) 2^n = (-2)^(-n)
n = 0 works, We get: 1 = 1
ELIMINATE C

D) (-2)^n = -(2^n)
n = 1 works, We get: -2 = -2
ELIMINATE D

E) (-2)^-n = -(2^-n)
n = 1 works, We get: -1/2 = -1/2
ELIMINATE E

So, the correct answer must be A

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by GMATGuruNY » Mon Oct 06, 2014 10:41 am
The problem should read as follows:
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.
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