Bunuel wrote:

Is \(xy \gt \frac{x}{y}\)?

(1) \(0 \lt y \lt 1\)

(2) \(xy \gt 1\)

Statement 1: implies that \(y\) is positive but nothing mentioned about \(x\).

InsufficientStatement 2: we need values of \(x\) & \(y\) to determine the value of \(\frac{x}{y}\). this statement implies that both \(x\) & \(y\) are of same sign but their values cannot be deduced.

InsufficientCombining 1 & 2, we know that \(y\) is positive so \(x\) is also positive and as \(y<1\) so it is reciprocal of any positive integer

so if \(x\) is integer for e.g \(x=2\) and \(y=\frac{1}{5}\), then \(xy=2*\frac{1}{5}=0.4\) but \(\frac{x}{y}=2/\frac{1}{5}=10\). Hence \(xy<\frac{x}{y}\)

and if \(x\) is not integer for e.g \(x=\frac{2}{5}\) and \(y=\frac{1}{2}\), then \(xy=\frac{2}{5}*\frac{1}{2}=0.2\) but \(\frac{x}{y}=\frac{2}{5}/\frac{1}{2}=0.8\). Hence \(xy<\frac{x}{y}\)

So we have a

NO for our question stem.

SufficientOption

C