If n is an integer and x^n – x^-n = 0, what is the value of x ?
(1) x is an integer.
(2) n ≠ 0
(1) x is an integer.
(2) n ≠ 0
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Source: Beat The GMAT — Data Sufficiency |
Reorganize stem asPAB2706 wrote:If n is an integer and x^n – x^-n = 0, what is the value of x ?
(1) x is an integer.
(2) n ≠ 0
X^n -1/X^n=0
X^2n=1
X=1^1/2n.
For all altegral n except 0, X=1. But for n=0 the equation has an indeterminate form X=1^1/0=1^infinity. Since interger 0 leads to an indeterminate form 1) is Not SUFF.
Under 2)
We are told n is not equal to 0. Well then X=1 for all other integral n. For n=-2, X=1^-1/4=1/(1^1/4 )=1. -1 is not a solution because every power of the form 1/p with p even, can be reduced to a base of the square root of -1 which is imaginary. For example -1^1/18= (-1^1/2)^1/9 and this gives imaginary number. If p is odd, the idea of multiplying odd number of negative numbers to produce a positive one is out of question. Since n can only take integral values, 2 is SUFF and 1 is the only solution of the equation.
Choose B
x^n - x^-n =0
---> x^2n - 1 = 0
1. x is an integer ... insuff... x can be 1 or -1; also n can take value = 0 then x can be anything
2. n is not 0, for any value of n, x can be 1 or -1...in suff
1. + 2. also doesn't help
E...
---> x^2n - 1 = 0
1. x is an integer ... insuff... x can be 1 or -1; also n can take value = 0 then x can be anything
2. n is not 0, for any value of n, x can be 1 or -1...in suff
1. + 2. also doesn't help
E...
