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B, C have can be equated by using n=0 D and E have external/independent -ve signs, so 0 wont help, but using n= +1 for D and -1 for E will equate the sides.

Each of the following has at least one solution EXCEPT [#permalink]
23 Aug 2012, 03:45

OA has to be A because Equation 1 simplifies to (2)^n (2)^n (-1)^n= -1 has no solution for any value of n Rest of options have at least 1 solution _________________

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all seems to have n=0 as solution....? whats the OA

\(n=0\) is not a solution of the equation \(-2^n = (-2)^{-n}\) (in fact this equation has no solution):

\(-2^n=-(2^n)=-(2^{0})=-1\) but \((-2)^{-n}=(-2)^{0}=1\).

Thank you for your response.

I would like to double check why we say that n=0 could be a solution in case of \((-2)^{-n}\) as \((-2)^{-n} = (-2)^{1/n}\) and then we can not divide by zero?

I would like to double check why we say that n=0 could be a solution in case of \((-2)^{-n}\) as \((-2)^{-n} = (-2)^{1/n}\) and then we can not divide by zero?

Nik

\((-2)^{-n} = 1/(-2)^n\) not \((-2)^{1/n}\) _________________

Why did you plug n=1 for the last two, wouldn't it be easier just to plug n=0 for all and see that A has no solution? Just want to know if there was any specific reason why you did so

Thank you Cheers J

PS. Would be nice if we could get this question in code format!

Why did you plug n=1 for the last two, wouldn't it be easier just to plug n=0 for all and see that A has no solution? Just want to know if there was any specific reason why you did so

Thank you Cheers J

PS. Would be nice if we could get this question in code format!

We need to find the equation that has no solution. What we are trying to do is find at least one solution for 4 equations. The fifth one will obviously not have any solution and will be our answer. Options (D) and (E) do not have 0 as a solution. So you try n = 1 on (A), (D) and (E). n = 1 is still not a solution for (A) but it is for (D) and (E).

(D) (–2)^n = –2^n When you put n = 0, you get (-2)^0 = -2^0 1 = -1 which doesn't hold. So you try n = 1 (–2)^1 = -2^1 -2 = -2 n = 1 is a solution.

Re: No solution N: Manhattan GMAT test [#permalink]
24 Aug 2014, 15:52

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Re: Each of the following equations has at least one solution [#permalink]
08 Sep 2015, 07:44

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