Data Sufficiency

akhilsuhag wrote:If x and y are positive integers, is x/y < (x+5)/(y+5) ?

Statement #1: y = 5
Statement #2: x > y

Target question: Is x/y < (x+5)/(y+5)?

This is a great candidate for REPHRASING the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

If y is a positive integer, then we can be certain that y and (y+5) are both POSITIVE. This allows us to safely multiply both sides of our inequality by y and (y+5).

Take x/y < (x+5)/(y+5) and multiply both sides by y to get: Is x < (y)(x+5)/(y+5)?
Then take x < (y)(x+5)/(y+5)? and multiply both sides by (y+5) to get: Is x(y+5) < (y)(x+5)?
Expand to get: Is xy + 5x < xy + 5y?
Subtract xy from both sides to get: Is 5x < 5y?
Divide both sides by 5 to get: Is x < y?

We now have a very simple, REPHRASED target question.....
REPHRASED target question: Is x < y?

Now onto the statements!

Statement 1: y = 5
Since we have no information about x, there's no way to tell whether or not x < y.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > y
Perfect!
If x > y then we can answer our REPHRASED target question with certainty.
NO, x is definitely not less than y.
So, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Hi akhilsuhag,

This DS question is great for TESTING Values, but there's also a hidden Number Property that makes dealing with Fact 2 easier than you might think.

We're told that X and Y are POSITIVE INTEGERS. We're asked if X/Y < (X+5)/(Y+5)? This is a YES/NO question.

*Brent's tactic to rewrite the question is quite useful, but not necessary to solve this problem*

Fact 1: Y = 5

With this information, we can rewrite the question as:

"Is X/5 < (X+5)/10?

Let's TEST Values...

If X = 1, is 1/5 < 6/10? The answer is YES.
If X = 5, is 5/5 < 10/10? The answer is NO.
Fact 1 is INSUFFICIENT

Fact 2: X > Y

Since both variables are POSITIVE INTEGERS and X > Y, we know that X+5 > Y+5 and we know that the numerator of both fractions is greater than the denominator.

Here's the Number Property I mentioned earlier: Since the numerator and denominator are both positive, ADDING the SAME value to both the numerator and the denominator will "push" the value of the fraction closer to 1.

eg 2/1 = 2

(2+1)/(1+1) = 3/2 = 1.5

(2+2)/(1+2) = 4/3 = 1.3333

(2+3)/(1+3) = 5/4 = 1.25

(2+4)/(1+4) = 6/5 = 1.2

Etc.

This ultimately means that, under these restrictions, X/Y will ALWAYS be greater than (X+5)/(Y+5), so the answer to the question will ALWAYS be NO.
Fact 2 is SUFFICIENT.

Final Answer: B

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

akhilsuhag wrote:If x and y are positive integers, is x/y < (x+5)/(y+5) ?

Statement #1: y = 5

Statement #2: x > y

Target question: Is x/y < (x+5)/(y+5)?

This is a great candidate for REPHRASING the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

If y is a positive integer, then we can be certain that y and (y+5) are both POSITIVE. This allows us to safely multiply both sides of our inequality by y and (y+5).

Take x/y < (x+5)/(y+5) and multiply both sides by y to get: Is x < (y)(x+5)/(y+5)?
Then take x < (y)(x+5)/(y+5) and multiply both sides by (y+5) to get: Is x(y+5) < (y)(x+5)?
Expand to get: Is xy + 5x < xy + 5y?
Subtract xy from both sides to get: Is 5x < 5y?
Divide both sides by 5 to get: Is x < y?

We now have a very simple, REPHRASED target question.....
REPHRASED target question: Is x < y?

Now onto the statements!

Statement 1: y = 5
Since we have no information about x, there's no way to tell whether or not x < y.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > y
Perfect!
If x > y then we can answer our REPHRASED target question with certainty: NO, x is definitely not less than y.
So, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent