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Magoosh GMAT Instructor
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If x and y are positive integers, is [#permalink]
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14 May 2013, 11:21
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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 < 5For the general method of solving questions such as this, without tedious plugandchug, see the following post: http://magoosh.com/gmat/2012/gmatshort ... enominatorMike
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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 < 5For the general method of solving questions such as this, without tedious plugandchug, see the following post: http://magoosh.com/gmat/2012/gmatshort ... enominatorMike 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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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



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Re: If x and y are positive integers, is [#permalink]
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15 May 2013, 04:06
madzstar wrote: 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. D. EACH 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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Re: If x and y are positive integers, is [#permalink]
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16 Dec 2014, 15:05
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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
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 3x2y<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. therefore answer is 'C'
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