integers

[CITI29]

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'.

[parallel_chase]

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.

[Vignesh.4384]

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

[parallel_chase]

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.

[Vignesh.4384]

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

[parallel_chase]

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.