x positive w negative

[iknownoone]

If x is a positive integer and w is a negative integer, what is the value of xw?

 

(1) x^w = 1/2

(2) w = -1

 

Please provide your explanations.

 

Thanks!

[manish8109]

Ans A

 

Stat 1:

 

x^w = 1/2= 2^(-1)

 

so, x=2 & w=-1

then,

xw=2*(-1)=-2-------sufficient

 

Stat 2:

 

w=-1

x^-1=1/x don't know what x is so insufficient

[safazal]

The Ans is A.

[Trouble]

if w is -ve and x is +ve,from

st1==> x^w=i/2==> x=2 and w=-1...x*w=-2==>suff.

 

w=-1 we know nothing about x so St2: insuff.

Answer (A)

[iknownoone]

The OA is A.

[Amilli]

Is there a methodical why at arriving at x=2 w=-1, because to me it doesn't seem that intuitive (I know,"what a dumb a**")

[genius_in_the_gene]

x^w=1/2=2^-1

Since w

x=2, w=-1

 

Hence A

[Amilli]

x^w=1/2=2^-1

Since w

x=2, w=-1

 

Hence A

 

I don't see a method there, you just wrote the ans... same one that had been posted a few times earlier with less explanation.

[e.cartman]

Stmt 1:

(pos int)^(neg int)

=1/(pos int)^(pos int)

Compare the denominator with 2. Since (pos int)^(pos int) always results in a pos int, which in this case is 2, how many ways are there to express 2 in that way?

Since sqrt(2), cuberoot(2), etc.. are all non-integers, you can't raise to any pos int higher than 1 like 2,3, etc. So there is unique solution.

If it had been 1/4 on RHS, then you would have got 2 solutions -- 4^-1 and 2^-2.

[12rk34]

Amilli,

I would like to clear your doubt.

x^w = 1/2 = 2^(-1)

This holds good here because we are given that x is +ve and w is -ve integer.

Let us see what other possibilities are:

1/2 = 8^(-1/3) = 512^(-1/9) ... etc.

Here x is +ve but w is a fraction.

Each of these possibilities does not satisfy the given conditon that x is +ve integer and w is a -ve integer. So except for x=2, w=-1 there is no other combination which satisfies this condition.

Hope it clears the doubt. :)

[Amilli]

Thanks guys, I do believed the ans was correct, I just wanted a methodical way to approach this type of problem, I mean it can make sense once you see the ans, but I want to know a reliable way to get there.

 

Cartman,

thanks your explanation is the best way i've seen to look at the problem.

 

thank you too 12rk34

[bose]

imo a