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If x, y, and c are positive, is (x+c)/(y+c)>x/y?

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MathRevolution
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If x, y, and c are positive, is (x+c)/(y+c)>x/y? [#permalink] New post  25 Feb 2016, 18:15
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72% (01:29) correct 28% (01:55) wrong based on 209 sessions

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If x, y, and c are positive, is (x+c)/(y+c)>x/y?

1) y>x
2) c>y


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BrentGMATPrepNow
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If x, y, and c are positive, is (x+c)/(y+c)>x/y? [#permalink] New post  25 Feb 2016, 19:31
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Quote:
If x, y, and c are positive, is (x+c)/(y+c) > x/y?

1) y > x
2) c > y



Target question: Is (x+c)/(y+c) > x/y?

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-data-sufficiency?id=1100

Given: x, y, and c are positive
This means that (y + c) is positive, which means we can take (x+c)/(y+c) > x/y and safely multiply both sides by (y + c) to get: (x+c) > (x/y)(y+c)
Also, since y is positive, we can safely multiply both sides by y to get: (y)(x+c) > (x)(y+c)
Expand to get: xy + yc > xy + xc
Subtract xy from both sides to get: yc > xc
Finally, divide both sides by c to get: y > x
So, we can REPHRASE the target question as.....
REPHRASED target question: Is y > x?

At this point, it will take no time at all to analyze the two statements.

Statement 1: y > x
PERFECT. This allows us to answer the REPHRASED target question with certainty.
So, statement 1 is SUFFICIENT

Statement 2: c > y
This does not help us answer the REPHRASED target question with certainty.
So, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
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chetan2u
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Re: If x, y, and c are positive, is (x+c)/(y+c)>x/y? [#permalink] New post  25 Feb 2016, 21:18
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MathRevolution wrote:
If x, y, and c are positive, is (x+c)/(y+c)>x/y?

1) y>x
2) c>y


* A solution will be posted in two days.


Hi,

Property of fraction


1)whenever you add the same amount to both denominator and numerator of a positive fraction, and fraction<1..
(x+c)/(y+c)>x/y

2)whenever you add the same amount to both denominator and numerator of a positive fraction, and fraction>1..
(x+c)/(y+c)<x/y..

here it is being asked, if fraction is<1..
so case 1, which requires denominator>numerator or y>x

what info do we require?


relation between x and y

lets see the statements..
1) y>x
gives a relation between x and y..
suff

2) c>y
does not give relation about x and y or any info to derive relation in x and y..
Insuff

A
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MathRevolution
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Re: If x, y, and c are positive, is (x+c)/(y+c)>x/y? [#permalink] New post  28 Feb 2016, 17:45
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x, y, and c are positive, is (x+c)/(y+c)>x/y?

1) y>x
2) c>y

-> If you modify the original condition and the question, they become (x+c)/(y+c)>x/y? -> y(x+c)>x(y+c)?, -> yx+yc>xy+xc?, yc>xc?(Since c>0, the direction of the inequality sign doesn’t change when dividing with C), which makes y>x?. Thus, A is the answer.
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warriorguy
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Re: If x, y, and c are positive, is (x+c)/(y+c)>x/y? [#permalink] New post  18 Oct 2016, 03:01
for a proper fraction, if the same value is added in N & D, fraction decreases than original fraction.

A is suff.

B doesn't give any info about X
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Re: If x, y, and c are positive, is (x+c)/(y+c)>x/y? [#permalink] New post  15 Jan 2023, 05:43
Hello from the GMAT Club BumpBot!

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Re: If x, y, and c are positive, is (x+c)/(y+c)>x/y? [#permalink]
15 Jan 2023, 05:43
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