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# If x and y are positive integers, is

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 3073
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Kudos [?]: 4456 [4] , given: 49

If x and y are positive integers, is [#permalink]

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14 May 2013, 11:21
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Difficulty:

35% (medium)

Question Stats:

73% (02:04) correct 27% (01:38) wrong based on 119 sessions

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If x and y are positive integers, is $$\frac{x}{y}<\frac{x+2}{y+3}$$?
Statement #1: y > 20
Statement #2: x < 5

For the general method of solving questions such as this, without tedious plug-and-chug, see the following post:
http://magoosh.com/gmat/2012/gmat-short ... enominator

Mike
[Reveal] Spoiler: OA

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Mike McGarry
Magoosh Test Prep

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Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 123
Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
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WE: Web Development (Computer Software)
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Kudos [?]: 95 [0], given: 14

Re: If x and y are positive integers, is [#permalink]

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14 May 2013, 12:04
mikemcgarry wrote:
If x and y are positive integers, is $$\frac{x}{y}<\frac{x+2}{y+3}$$?
Statement #1: y > 20
Statement #2: x < 5

For the general method of solving questions such as this, without tedious plug-and-chug, see the following post:
http://magoosh.com/gmat/2012/gmat-short ... enominator

Mike

Lemme verify my procedure here! According to the post, for x/y being a proper fraction will go closer to a/b if the operation x+a/y+b is performed. And as always $$x/y < x+a/y+b$$. The values still go closer to 1 for improper fraction but, $$x/y > x+a/y+b$$!

So, by combining both the statements we confirm that x/y is always less than 5/20 i.e. 1/4 and Hence a proper fraction. Hence if I am to add 2 in the numerator and 3 to the denom, the fraction will approach 2/3. Hence the answer derived, $$x+2/y+93 > x/y$$:) *Please correct me If I am wrong *

Def better than the plug and chug would have taken me a long time to figure this one out by the normal way Wonderful method Mike!

Regards,
Arpan
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Feed me some KUDOS! *always hungry*

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Joined: 24 Apr 2013
Posts: 54
Schools: Duke '16
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Kudos [?]: 9 [0], given: 76

Re: If x and y are positive integers, is [#permalink]

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14 May 2013, 15:29
a= statment 1 alone sufficient

b= statment 2 alone is sufficient

c= both statments together are sufficient

d= both statment together are insufficient

e= none of the above

right? am i right will all of the following cause i end up guessing alot
Math Expert
Joined: 02 Sep 2009
Posts: 33062
Followers: 5775

Kudos [?]: 70858 [0], given: 9857

Re: If x and y are positive integers, is [#permalink]

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15 May 2013, 04:06
Expert's post
a= statment 1 alone sufficient

b= statment 2 alone is sufficient

c= both statments together are sufficient

d= both statment together are insufficient

e= none of the above

right? am i right will all of the following cause i end up guessing alot

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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Kudos [?]: 2 [1] , given: 2

Re: If x and y are positive integers, is [#permalink]

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16 Dec 2014, 15:05
1
KUDOS
1
This post was
BOOKMARKED
If x and y are positive integers, is \frac{x}{y}<\frac{x+2}{y+3}?
Statement #1: y > 20
Statement #2: x < 5

solution:

since x and y are positive, then we can cross multiply the questions:

is x(y+3) < y(x+2)?
is xy+3x < xy + 2y?
is 3x<2y?
is 3x-2y<0?

basically the question is asking if x<y?

from the statements, none is sufficient to answer the question alone. combining the two, we can conclusively conclude that x < y.

Give kuddos if you like my explanation!
Re: If x and y are positive integers, is   [#permalink] 16 Dec 2014, 15:05
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