Bunuel wrote:

Is rst = 1 ?

(1) \(r\sqrt{t} =\frac{s\sqrt{t}}{s}\)

(2) \(\frac{rt}{\sqrt{t}}=\frac{\sqrt{t}}{st}\)

As this looks to be a very technical question (with many equations), we'll just solve it.

This is a Precise approach.

(1) We can cancel out \(s\) from the right-hand side giving \(r\sqrt{t} =\sqrt{t}\)

As we don't know if \(t = 0\) or not, we can't cancel it out but we can rewrite as \(r\sqrt{t} -\sqrt{t}=0\)

This simplifies to \(\sqrt{t}(r-1)=0\) meaning that \(t = 0\) or \(r = 1\).

Insufficient!

(2) Since both \(s\) and \(t\) are in the denominator, they can't be equal to 0 so we can multiply by them.

Multiplying by \(s\) and by \(\sqrt{t}\) gives \(rst = \frac{t}{t}=1\)

Sufficient!

(B) is our answer.

"2) Since both ss and tt are in the denominator, they can't be equal to 0 so we can multiply by them.