Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 Dec 2013, 00:47

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x and y are positive integers, is (2 + x)/(3 + y) greater

Author Message
TAGS:
Director
Joined: 29 Nov 2012
Posts: 940
Followers: 10

Kudos [?]: 135 [2] , given: 543

If x and y are positive integers, is (2 + x)/(3 + y) greater [#permalink]  12 Mar 2013, 02:48
2
KUDOS
00:00

Difficulty:

25% (low)

Question Stats:

63% (02:14) correct 36% (01:08) wrong based on 60 sessions
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

Can we cross multiply in this question? Suppose it wasn't given positive then we move the variables to one side and solve?
[Reveal] Spoiler: OA

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Last edited by Bunuel on 12 Mar 2013, 02:58, edited 1 time in total.
EDITED THE QUESTION.
Math Expert
Joined: 02 Sep 2009
Posts: 15204
Followers: 2558

Kudos [?]: 15808 [4] , given: 1572

Re: If x and y are positive integers, is (2 + x)/(3 + y) greater [#permalink]  12 Mar 2013, 03:08
4
KUDOS
Expert's post
If x and y are positive integers, is (2 + x)/(3 + y) greater than (2 + y)/(3 + x)?

Is \frac{2 + x}{3 + y}>\frac{2 + y}{3 + x}? Since both denominators are positive we can safely cross-multiply. Though we can solve the question without doing that.

(1) x + y = 3. If x=1 and y=2, then the answer is NO (3/5<4/4) but if x=2 and y=1, then the answer is YES (4/4>3/5). Not sufficient.

(2) x > y. This implies that the numerator of LHS is more than the numerator of RHS, and the denominator of LHS is less than the denominator of RHS, which means that LHS > RHS. Sufficient.

Hope it's clear.
_________________
Intern
Status: pursuing a dream
Joined: 02 Jun 2011
Posts: 45
Schools: MIT Sloan (LGO)
Followers: 1

Kudos [?]: 28 [0], given: 7

Re: If x and y are positive integers, is (2 + x)/(3 + y) greater [#permalink]  17 Mar 2013, 07:36
Bunuel wrote:
If x and y are positive integers, is (2 + x)/(3 + y) greater than (2 + y)/(3 + x)?

Is \frac{2 + x}{3 + y}>\frac{2 + y}{3 + x}? Since both denominators are positive we can safely cross-multiply. Though we can solve the question without doing that.

(1) x + y = 3. If x=1 and y=2, then the answer is NO (3/5<4/4) but if x=2 and y=1, then the answer is YES (4/4>3/5). Not sufficient.

(2) x > y. This implies that the numerator of LHS is more than the numerator of RHS, and the denominator of LHS is less than the denominator of RHS, which means that LHS > RHS. Sufficient.

Hope it's clear.

Dear Bunuel,

Can you please elaborate on an Algebra approach?

So far I'd go like this:

Since we know that the denominators are positive, we can cross multiply:

x^2+5x<y^2+5y

x^2-y^2<5y-5x

(x+y)(x-y)<5(y-x)

(x+y)(x-y)<-5(x-y)

Here, can we divide by (x-y)? If not, how to continue?
Manager
Joined: 14 Aug 2005
Posts: 87
Followers: 0

Kudos [?]: 6 [0], given: 2

Re: If x and y are positive integers, is (2 + x)/(3 + y) greater [#permalink]  18 Mar 2013, 21:57
Not sure if you would really like to take the algebra approach.

The question is pretty much clear about the usage of positive integer. So lets take a small set of positive integers {1,2,3,4}

Now, for us to get 2+x > 3+y we need to have only x>y; thats the only condition which can help us solve the equation. Since, that's given in B! Hence, B is the answer
_________________

One Last Shot

SVP
Joined: 05 Jul 2006
Posts: 1554
Followers: 4

Kudos [?]: 48 [0], given: 39

Re: If x and y are positive integers, is (2 + x)/(3 + y) greater [#permalink]  20 Mar 2013, 02:02
[quote="fozzzy"]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

x,y +ve intigers

from 1

x,y are in fact 1,2 but we dont know which is which...insuff

from 2

if x>y then : numerator 2+x >2+y ( numerator of each side) and 3+y<3+x (denominator of each side), thus larger numerator/smaller denominator is surely > smaller numerator/ larger denominator ..hope this makes sense
Math Expert
Joined: 02 Sep 2009
Posts: 15204
Followers: 2558

Kudos [?]: 15808 [0], given: 1572

Re: If x and y are positive integers, is (2 + x)/(3 + y) greater [#permalink]  20 Mar 2013, 04:06
Expert's post
LGOdream wrote:
Bunuel wrote:
If x and y are positive integers, is (2 + x)/(3 + y) greater than (2 + y)/(3 + x)?

Is \frac{2 + x}{3 + y}>\frac{2 + y}{3 + x}? Since both denominators are positive we can safely cross-multiply. Though we can solve the question without doing that.

(1) x + y = 3. If x=1 and y=2, then the answer is NO (3/5<4/4) but if x=2 and y=1, then the answer is YES (4/4>3/5). Not sufficient.

(2) x > y. This implies that the numerator of LHS is more than the numerator of RHS, and the denominator of LHS is less than the denominator of RHS, which means that LHS > RHS. Sufficient.

Hope it's clear.

Dear Bunuel,

Can you please elaborate on an Algebra approach?

So far I'd go like this:

Since we know that the denominators are positive, we can cross multiply:

x^2+5x<y^2+5y

x^2-y^2<5y-5x

(x+y)(x-y)<5(y-x)

(x+y)(x-y)<-5(x-y)

Here, can we divide by (x-y)? If not, how to continue?

First of all, is (2 + x)/(3 + y) greater than (2 + y)/(3 + x)? Means is \frac{2 + x}{3 + y}>\frac{2 + y}{3 + x}?

Cross-multiply: is (2+x)(3+x)>(2+y)(3+y) --> is 5x+x^2>5y+y^2? --> is (x-y)(x+y)>-5(x-y)? Here we cannot divide by x-y, since we don't know whether it's positive or negative.

What we can do is: (x-y)(x+y)>-5(x-y)? --> (x-y)(x+y)+5(x-y)>0? --> (x-y)(x+y+5)>0?

(1) x + y = 3. The question becomes: is (x-y)(3+5)>0? --> is x-y>0? We don't know that, thus this statement is not sufficient.

(2) x > y --> x-y>0. So, we can reduce by x-y and the question becomes: is x+y+5>0? Since x and y are positive then the answer to this question is YES. Sufficient.

Hope it helps.
_________________
Re: If x and y are positive integers, is (2 + x)/(3 + y) greater   [#permalink] 20 Mar 2013, 04:06
Similar topics Replies Last post
Similar
Topics:
1 x^3*y ^4=5000, y =? 1)y is a positive integer 2)x is a 5 25 Jun 2004, 12:14
ds.x^3*y ^4=5000, y =? 1) y is a positive integer 2) x is a 6 09 Sep 2004, 20:41
(x^3 * y ^4=5000, y = ? 1)y is a positive integer 2)x is a 6 08 Feb 2005, 13:52
If (2^x)(3^y)=288 where x and y are positive integers then 5 07 Jan 2006, 14:05
If x is a positive integer, is y^2 (x^3 - x + 1) 4 01 Oct 2008, 23:00
Display posts from previous: Sort by