Stmt I)
x is an integer
since n value is not given if n was 0 then x could be any integer
Stmt II
n <>0
Gives us no definite value of x even wihtout knowing x is an intger or not we can have x=-1 or x=1
Stmt I and Ii put together still not sufficient
I go for E
It could be 1 or -1 (both statements put together are not sufficient)
Hope I dint miss something!
x^(n) – x^(-n) = 0
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Source: Beat The GMAT — Data Sufficiency |
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jsl
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good question...
I simplified question stem to:
( x^2n - 1 )/(x^n) = 0
x^2n = 1
Given x^2n = 1
There are only 2 ways of getting x^2n to equal 1. That is if x = 1 and n = 0 or x = 0 and n=1 (I THINK!). I wish I could remember the exponent rules surrounding 0's and 1's.
I think...
1^0 = 1
2^0 = 1
3^0 = 1, etc....
and...
0^1 = 1
0^2 = 1
0^3 = 1, etc....
Therefore, I'm guessing B...
I simplified question stem to:
( x^2n - 1 )/(x^n) = 0
x^2n = 1
Given x^2n = 1
There are only 2 ways of getting x^2n to equal 1. That is if x = 1 and n = 0 or x = 0 and n=1 (I THINK!). I wish I could remember the exponent rules surrounding 0's and 1's.
I think...
1^0 = 1
2^0 = 1
3^0 = 1, etc....
and...
0^1 = 1
0^2 = 1
0^3 = 1, etc....
Therefore, I'm guessing B...
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scoobydooby
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jsl, 0^1, 0^ (anything) would be 0jsl wrote:good question...
I simplified question stem to:
( x^2n - 1 )/(x^n) = 0
x^2n = 1
Given x^2n = 1
There are only 2 ways of getting x^2n to equal 1. That is if x = 1 and n = 0 or x = 0 and n=1 (I THINK!). I wish I could remember the exponent rules surrounding 0's and 1's.
I think...
1^0 = 1
2^0 = 1
3^0 = 1, etc....
and...
0^1 = 1
0^2 = 1
0^3 = 1, etc....
Therefore, I'm guessing B...
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scoobydooby
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i would think E
if x^n-x^(-n)=0 then x^n=x^(-n) or x^n=1/(x^n)
x cannot be 0 or 1/0 would be undefined, so possibilities are n=0, x=1 or x=-1(provided n is even)
1) x is an integer, it may be that x=1 or -1, we dont know n either. not sufficient
2) n is not 0, so x can be 1 or -1 depending on whether n is even or odd. not sufficient
combining x is an integer, n not zero, we still do not know if n is even or odd, x=1 or -1. therefore E
if x^n-x^(-n)=0 then x^n=x^(-n) or x^n=1/(x^n)
x cannot be 0 or 1/0 would be undefined, so possibilities are n=0, x=1 or x=-1(provided n is even)
1) x is an integer, it may be that x=1 or -1, we dont know n either. not sufficient
2) n is not 0, so x can be 1 or -1 depending on whether n is even or odd. not sufficient
combining x is an integer, n not zero, we still do not know if n is even or odd, x=1 or -1. therefore E
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logitech
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JSL, thanks for the explanation.jsl wrote:good question...
I simplified question stem to:
( x^2n - 1 )/(x^n) = 0
x^2n = 1
Given x^2n = 1
There are only 2 ways of getting x^2n to equal 1. That is if x = 1 and n = 0 or x = 0 and n=1 (I THINK!). I wish I could remember the exponent rules surrounding 0's and 1's.
I think...
1^0 = 1
2^0 = 1
3^0 = 1, etc....
and...
0^1 = 1
0^2 = 1
0^3 = 1, etc....
Therefore, I'm guessing B...
( x^2n - 1 )/(x^n) = 0
x^2n = 1
And we have to keep in mind that X^n can not be equal to ZERO
So this leaves us:
either x = -1 or + 1 and n is any integer but ZERO
OR X is ANY INTEGER and n is ZERO
1) Insuff
2) Suff , because it tells us n ≠ 0 and eliminates of of the choices.
by the way, if I remember correctly
0^1 = 1
0^2 = 0
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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"DON'T LET ANYONE STEAL YOUR DREAM!"
According to a check on my TI-84 0^any number = 0
I think B is insufficient because also because it only tells us that n is not equal to 0.
Therefore given x^2n = 1
1^any number = 1
however x could also be -1 because n could be 2, 4, 6, etc.
therefore 2 is insuff also.
I go with E also.
I think B is insufficient because also because it only tells us that n is not equal to 0.
Therefore given x^2n = 1
1^any number = 1
however x could also be -1 because n could be 2, 4, 6, etc.
therefore 2 is insuff also.
I go with E also.
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logitech
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Exponentiation: x0 = 1, except that the case x = 0 may be left undefined in some contexts; see Zero to the zero power. For all positive real x, 0x = 0.cramya wrote:One samll caveat: 0 ^ 0 would be undefined if I am not mistaken
https://en.wikipedia.org/wiki/Zero
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"
