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impulse responses (1/2)

^{n}u(n) and (1/3)

^{n}u(n-1). A tone at 1 kHz is attenuated by 43.6%. Can you tell what the sampling rate is?

My thought process..

I have only solved problems where I had to find the attenuation given the frequency of the tone, the signal bandwidth, and the sampling rate, I am not sure about the posed question. At first I thought yes, it can be found because you can find the transfer function and from this find the steady state and solve for the sampling rate by setting the steady state equal to the attenuation. However, I tried doing the actual calculation and got stuck (I believe this is why we aren't expected to find the actual value). Then I thought... Do you need to know the bandwidth of the system to find the sampling rate? Isn't the sampling rate equal to 2*bandwidth?