Can someone show me a short cut method to solve the below question ?

Q. If x and y are positive integers, is (2+x)/(3+y) greater than (2+y)/(3+x) ?

(1) x+y =3

(2) x>y

OA B

Thank You

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- Brent@GMATPrepNow
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Target question: Is (2+x)/(3+y) greater than (2+y)/(3+x) ?Param800 wrote:Can someone show me a short cut method to solve the below question ?

Q. If x and y are positive integers, is (2+x)/(3+y) greater than (2+y)/(3+x) ?

(1) x+y =3

(2) x>y

OA B

Thank You

In other words, is (2+x)/(3+y) > (2+y)/(3+x)?

If x and y are both positive, then the denominators on both sides of the inequality are positive. This means we can simplify the target question by multiplying both sides by (3+y)(3+x) to get:

Is (2+x)(3+x) > (2+y)(3+y)?

To further simplify the target question, we'll first expand both sides to get:

Is 6 + 5x + x^2 > 6 + 5y + y^2

Simplify to get: Is 5x + x^2 > 5y + y^2

Notice that this inequality will true if x > y

Rephrased target question:

**Is x > y ?**

Statement 1: x+y =3

There are several pairs of values that meet this condition. Here are two:

Case a: x=2 and y=1, in which case x is greater than y

Case b: x=1 and y=2, in which case x is not greater than y

Since we cannot answer the rephrased target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x>y

This definitely helps us answer our rephrased target question with certainty.

So, statement 2 is SUFFICIENT

Answer = B

Cheers,

Brent

Last edited by Brent@GMATPrepNow on Wed Jan 09, 2013 10:08 am, edited 1 time in total.

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Since x>0 and y>0, 2+x, 3+y, 2+y, and 3+x are all POSITIVE.Param800 wrote:Can someone show me a short cut method to solve the below question ?

Q. If x and y are positive integers, is (2+x)/(3+y) greater than (2+y)/(3+x) ?

(1) x+y =3

(2) x>y

OA B

Thank You

This means we can rephrase the question stem by cross-multipying:

(2+x) / (3+y) > (2+y) / (3+x) ?

(2+x)(3+x) > (2+y)(3+y)

6 + 5x + xÂ² > 6 + 5y + yÂ²

5x + xÂ² > 5y + yÂ² ?

The lefthand side will be greater than the righthand side if x > y.

Question rephrased: Is x > y?

**Statement 1: x+y = 3**

If x=2 and y=1, then x>y.

If x=1 and y=2, then x<y.

INSUFFICIENT.

**Statement 2: x>y**

SUFFICIENT.

The correct answer is C.

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Followed here and elsewhere by over 1900 test-takers.

I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.

My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.

I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].

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### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

I've edited my post accordingly.

Cheers,

Brent