Hi,
Can someone confirms that 2^-0 is not 2/0 but rather 1 just as per 2^0?
Each of the following equations has at least one solution EXCEPT
-2^n = (-2)^-n
2^-n = (-2)^n
2^n = (-2)^-n
(-2)^n = -2^n
(-2)^-n = -2^-n
Answer is a.
Thx
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2^(-0) = 1/[2^0] = 1/1 = 1claudayst wrote:Can someone confirms that 2^-0 is not 2/0 but rather 1 just as per 2^0?
A) -2^n = (-2)^-n ---> -2^n = 1/[(-2)^n] ---> -[(2^n)*((-2)^n)] = 1 ---> (-4)^n = -1 ---> [(-1)^n]*[4^n] = -1claudayst wrote:Each of the following equations has at least one solution EXCEPT
Now, now the sign of the LHS will be negative only if n is some odd integer. But if n is some odd integer, magnitude of the LHS cannot be equal to 1.
Hence, there is no solution for A and as there will be only one correct option, we don't need to check other options.
The correct answer is A.
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LHS --> Left hand side of an equationclaudayst wrote:Thank you.
What do you mean by LHS?
RHS --> Right hand side of an equation
Anju Agarwal
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- GMATGuruNY
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For many test-takers, the most practical approach will be to eliminate the four answer choices that DO have at least one solution.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
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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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].
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