If x, y, and z are positive numbers, is x - y < z ?

[BTGModeratorVI]

If x, y, and z are positive numbers, is x - y < z ?

(1) x + y < z
(2) xy < z^2

Answer: A
Source: Economist GMAT

[Brent@GMATPrepNow]

If x, y, and z are positive numbers, is x - y < z ?

(1) x + y < z
(2) xy < z^2

Answer: A
Source: Economist GMAT

Given: x, y, and z are POSITIVE numbers

Target question: Is x - y < z?

Statement 1: x + y < z
The most important thing here is that y is POSITIVE
If y is positive, then we can be certain that x < x + y
Conversely, if y is positive, then we can be certain that x - y < x
When we combine the two inequalities, we get: x - y < x < x + y
Most importantly, this means that: x - y < x + y

Statement 1 tells us that: x + y < z
So we can add this to our inequality to get: x - y < x + y < z
At this point, we can be certain that x - y < z
In other words, the answer to the target question is YES, x - y is less than z
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: xy < z²
There are several values of x, y and z that satisfy statement 2. Here are two:
Case a: x = 1, y = 1 and z = 2 (these values satisfy the condition that xy < z²). In this case, the answer to the target question is YES, x - y is less than z
Case b: x = 30, y = 1 and z = 10 (these values satisfy the condition that xy < z²). In this case, the answer to the target question is NO, x - y is not less than z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent