BTGModeratorVI wrote: ↑Thu Jun 11, 2020 8:49 am
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
