Data Sufficiency

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

lionsshare wrote:If x and y are positive, is x/y greater than 1 ?

(1) xy > 1
(2) x - y > 0

OA: B

Anyone, please what's the solution to the problem. Bunch of thanks!

Slight variation on Brent's explanation...

We rephrase the target question from the beginning as:
is x/y > 1 --> is x > y ?
(Because we know that both x and y are positive, we can multiply both sides by y). We are looking for a RELATIVE relationship between x and y.

(1) xy > 1
Knowing something about the product of the two tells us nothing about the RELATIVE sizes of x and y. We can have a product greater than 1 with a larger x or with a larger y.
Insufficient.

(2) x - y > 0
Add y to both sides: x > y
Since this gives us exactly our target question, it's sufficient.

The answer is B.

lionsshare wrote:If x and y are positive, is x/y greater than 1 ?

(1) xy > 1
(2) x - y > 0

We are asked is x/y > 1?

Since x and y are positive we can multiply both sides of our inequality by y to obtain:

Is x > y?

Statement One Alone:

xy > 1

Knowing that the product of xy is greater than 1 does not allow us to determine whether x is greater than y.

For example, if x = 2 and y = 1, then x > y, but if x = 1 and y = 2, then x < y.

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x - y > 0

We can add y to both sides of the inequality to obtain:

x > y

Statement two is sufficient to answer the question.

Answer: B