Data Sufficiency

Hi Manonamission,

To start, this question should have been posted in the DS forum. That having been said, you can solve it rather easily by TESTing VALUES and thinking about the Number Properties involved.

We're told that X and Y are POSITIVE. We're asked if X/Y is greater than 1. This is a YES/NO question.

1) (X)(Y) > 1

IF.... X=2, Y=1, then the answer to the question is YES.
IF.... X=1, Y=2, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) (X - Y) > 1

Since we know that X and Y are both POSITIVE, then Fact 2 proves that X > Y. Under these restrictions, X/Y will ALWAYS be greater than 1, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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

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

Here's a different approach with regards to statement 2...

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

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

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

We need to determine whether x/y > 1. Since we know that x and y are positive, we can adjust question to ask: is x > y ?

Statement One Alone:

xy > 1

Knowing that xy > 1 is not enough information to determine whether x is greater than y.

For example, x could be 2 and y could be 1, in which case x IS greater than y; or x could be 1 and y could be 2, in which case x IS NOT greater than y.

Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

x - y > 1

We can manipulate the inequality in statement two to read: x > y + 1. Since we know that x is greater than y + 1, x must always be greater than y. Statement two is sufficient to answer the question.

Answer: B