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Each of the following equations has at least one solution EXCEPT
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12 May 2010, 09:12
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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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Re: Each of the following equations has at least one solution EXCEPT
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12 May 2010, 14:01




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Re: Each of the following equations has at least one solution EXCEPT
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12 May 2010, 10:53
marcusaurelius wrote: 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 IMHO A a) –2^n = (–2)^n –2^n = 1/(–2)^n –2^n * (–2)^n = 1, Keep it. Let's solve the other options..!! b) 2^n = (–2)^n 1/2^n = (–2)^n 1 = (–2)^n * (2^n) For n=0, L.H.S = R.H.S c) 2^n = (–2)^n 2^n = 1/ (–2)^n (2^n) * (–2)^n = 1 For n=0, L.H.S = R.H.S d) (–2)^n = –2^n (–2)^n / –2^n = 1 For n=1, L.H.S = R.H.S e) (–2)^n = –2^n 1/ (–2)^n = 1/–2^n For n=1, L.H.S = R.H.S




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Re: Each of the following equations has at least one solution EXCEPT
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12 May 2010, 11:09
all seems to have n=0 as solution....? whats the OA
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Re: Each of the following equations has at least one solution EXCEPT
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12 May 2010, 15:13
yes right i didnt read it closely
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Re: Each of the following equations has at least one solution EXCEPT
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14 May 2010, 06:56
Hi, it's really elegant question 0 is a solution for second and third equations. 1 is a solution for the last two equations. So answer is A. Really if n is not equal to 0 then absolute value of left part is greater than 1 and right part is less than 1. In case when n is equal to 0 we will get 1=1.
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Re: Each of the following equations has at least one solution EXCEPT
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14 May 2010, 12:49
great explanation Bunuel, thanks



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Re: Each of the following equations has at least one solution EXCEPT
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15 Jun 2010, 13:15
Thanks for merging.
Do you mean a negative number raised to the power of 0 yields 1?? I didn't know that!



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Re: Each of the following equations has at least one solution EXCEPT
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15 Jun 2010, 22:56
So how do you know that the point here is that 2^n means (2^n) and not (2)^n
The actual question has no parenthesis. This is tricky!



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Re: Each of the following equations has at least one solution EXCEPT
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06 Dec 2010, 08:21
SubratGmat2011 wrote: 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
Can somebody plz help me out what is the approch for this type of problems? The first and most straight forward approach that comes to mind is that I can see most of these equations will have n = 0 or n = 1 as a solution. Except for the very first one: n = 0: 2^0 = 1 while (2)^(0) = 1 n = 1: 2^1 = 2 while (2)^n = 1/2 For all other options, n = 0 or 1 satisfies the equation.
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Re: Each of the following equations has at least one solution EXCEPT
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19 Jan 2011, 22:03
Lets look at each choice  A –2^n = (–2)^n =>(1).(2)^n = 1/(2)^n =>(1).(2)^n.(2)^n = 1 =>(1).(2)^n.(1)^n.(2)^n = 1 =>(1).(1)^n.(2)^2n = 1 Above cannot be true for any value of n (No solution  answer) B 2^n = (–2)^n =>1/(2)^n = (2)^n =>1=(1)^n.(2)^n.(2)^n =>1=(1)^n.(2)^2n Above is true for n=0, so it has atleast one solution C 2^n = (–2)^n =>(2)^n = 1/(2)^n Rest of the steps Similar to option B D (–2)^n = –2^n =>(1)^n. (2)^n = (1).(2)^n =>(1)^n = (1) Above is true for all odd values of n E (–2)^n = –2^n =>1/[(1)^n. (2)^n] = (1)/(2)^n =>1/[(1)^n] = (1) =>1/(1)^n = 1 Above is true for all odd values of n I hope this helps.
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Re: Each of the following equations has at least one solution EXCEPT
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18 Feb 2011, 10:22
i guess the only real way to solve it under 2 min is to plug in 0/1... if u start with choosing 1 here as first step is not good... choosing 0 is canceling 3 choices quickly...
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Re: Each of the following equations has at least one solution EXCEPT
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05 May 2011, 17:26
lets pick a value for n.
n = 0
A. cannot be true as we get 1 on LHS and 1 on RHS ( as anything to the power of 0 is 1) B. true (LHS = RHS = 1) C. true (LHS = RHS = 1) D. true (LHS = RHS = 1) E. true (LHS = RHS = 1)
Answer is A.



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Re: Each of the following equations has at least one solution EXCEPT
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05 May 2011, 22:42
for B and C n = 0 for D and E n = 1.
A prevails.



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Re: Each of the following equations has at least one solution EXCEPT
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18 Aug 2012, 15:14
arichardson26 wrote: Each of the following 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 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. Took more than 2 mins
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Re: Each of the following equations has at least one solution EXCEPT
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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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Re: Each of the following equations has at least one solution EXCEPT
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14 Oct 2012, 07:05
Bunuel wrote: gurpreetsingh wrote: 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? Nik



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Re: Each of the following equations has at least one solution EXCEPT
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14 Oct 2012, 22:12
NikRu wrote: 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 \((2)^{1/n}\)
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Re: Each of the following equations has at least one solution EXCEPT &nbs
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