Data Sufficiency

If n is an integer and (x^n)-(x^-n)=0, what is the value of x?

1)x is an integer
2)n is not equal to 0.

Pls explain why the ans cant be 'b'. Correct ans given is 'e'.

first simplify the equation.

(x^n) - (1/x^n)=0

Statement I.

x is an integer. Insufficient we dont know anything about n.

Statement II.

n is not equal to 0.

Plug in numbers.
x=1
n=2
1^2 - (1/1^2) = 0
1-1=0
0=0

x=2
n=2

2^2 - (1/2^2) = 3/4 is not equal to 0

hence insufficient.

Even after combining both the statements we cannot get anything different from what is shown above, hence answer is E.

Hi parallel_chase,

parallel_chase Posted: Mon Aug 04, 2008 12:59 am Post subject:

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first simplify the equation.

(x^n) - (1/x^n)=0 ------------------------------ eq1

Can we simplify this as below ?
taking lcm of the above eq1

{(x^n)(x^n) -1 }/(x^n) = 0

Therefore x^2n - 1 = 0

x^2n = 1 ----------------------------------- eq2

Wen we try to plug in values into this eq2 .. then we can say that x has 2 be 1 right ?

Thanks,
Vignesh

Can we simplify this as below ?
taking lcm of the above eq1

{(x^n)(x^n) -1 }/(x^n) = 0

Therefore x^2n - 1 = 0

x^2n = 1 ----------------------------------- eq2

Wen we try to plug in values into this eq2 .. then we can say that x has 2 be 1 right ?

What you are doing is right.
But the statement will still not be sufficient.

X=1
n=2


1^4 =1
1=1
LHS=RHS

x=2
n=1

2^2=1
4=1
4 is not equal to 1

Hence insufficient.

Always analyze different possibilities for the same variable. Especially in DS.

Hey parallel_chase,

I stil have a doubt
I dont think it works the way u have explained.

statement B says N is not equal to zero.
So for the LHS to be equal to RHS the value of X can take the value "1" only. Since only 1^n is 1.

Do u understand what i am trying to say ?

Regards,
Vignesh

Vignesh.4384 wrote:Hey parallel_chase,

I stil have a doubt
I dont think it works the way u have explained.

statement B says N is not equal to zero.
So for the LHS to be equal to RHS the value of X can take the value "1" only. Since only 1^n is 1.

Do u understand what i am trying to say ?

Regards,
Vignesh

You are right I misinterpreted the question, i was just trying to prove the statement instead we need to find the value of x.

Anyways,


Even if we simplify the statement

x^2n =1

we still get two values i.e. x=1 or -1
Since the power is even for x^2n , for any of the two values of x i.e. 1 or -1, the result will always be 1.

Hence Insufficient.

Even combining both the statements together, we cannot conclude anything hence E is the answer.

Thanks.