1. No info about y. INSUFF

2. 1/x < y
1 < xy if x is +ve, 1 > xy if x is -ve. No info about x's sign. INSUFF.

Combining 1 & 2, we get the xy > 1.

Hence C.

ArunangsuSahu wrote:x not equal to 0. is xy>1?
(1) x>1
(2)1/x<y

For xy>1 , we know that both x and y should either be positive or negative.

St.1 x>1, nothing about y. Insufficient.

St.2 1/x<y, we don't know whether x is positive or negative, so we can't determine because we cannot multiply both sides of the inequality without knowing the sign. If x is positive then it will be 1<xy we don't have to flip the sign if we multiply both sides of the inequality by x. But if x is negative, we have to flip the sign of inequality and it will be 1>xy by multiplying both sides by -x.

Taking both, we know from St.1 that x>1, that is x is positive, so from St.2 if we multiply both sides of the inequality by x we get 1<xy or xy>1. Sufficient.

Ans. C

Another approach:

Stmt 1: x > 1 not sufficient since not clear what's the value of y. INSUFFICIENT

Stmt 2: 1/x < y can be rewritten as:
y - 1/x >0 => (xy-1)/x >0.
The above can only be true when xy > 1 AND x > 0 OR xy < 1 AND x < 0.
Thus we see that depending on x > or < 0 xy > or < 1. INSUFFICIENT

Stmt 1 and 2: x >1 implies x >0, thus from Stmt 2 analysis above, when x > 0, xy > 1. SUFFICIENT.

Hence C

OA is (C)