Is x < 1/y?

[BTGModeratorVI]

Is x < 1/y?
1) y > 0
2) xy < 1

Answer: C
Source: Math Revolution

[Brent@GMATPrepNow]

Is x < 1/y?
1) y > 0
2) xy < 1

Answer: C
Source: Math Revolution

Target question: Is x < 1/y?

Statement 1: y > 0
No information about x, so statement 1 is NOT SUFFICIENT

Statement 2: xy < 1
IMPORTANT: some students will want to divide both sides by y to get x < 1/y, HOWEVER doing so is incorrect, because we don't know whether y is POSITIVE or NEGATIVE.
If y is POSITIVE, then dividing both sides by y gives us x < 1/y
If y is NEGATIVE, then dividing both sides by y gives us x > 1/y [when we divide both sides by a negative value, we must REVERSE the direction of the inequality]
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that y is POSITIVE
Statement 2 tells us that xy < 1
Since we know that y is POSITIVE, we can safely divide both sides by y to get the inequality x < 1/y.

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent