lionsshare wrote:If x and y are positive, is x/y greater than 1 ?
(1) xy > 1
(2) x - y > 0
Target question: Is x/y > 1?
Given: x and y are positive
Statement 1: xy > 1
This statement doesn't
FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 2. Here, x/y = 1/2,
which means x/y < 1
Case b: x = 2 and y = 1. Here, x/y = 2/1 = 2,
which means x/y > 1
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: x-y > 1
With this statement, it might be useful to consider
rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Since x and y are positive, we can take the inequality
x/y > 1 and multiply both sides by y to get:
x > y.
Now let's subtract both sides by y to get:
x - y > 0
So, let's REPHRASE the target question...
REPHRASED target question: Is x-y > 0?
Statement 2 tells us that x - y > 1
Since 1 > 0, we can say that x - y > 1 > 0
So, we can conclude that
x - y > 0
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
