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If x, y, and c are positive, is (x+c)/(y+c)>x/y? 1) y>

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If x, y, and c are positive, is (x+c)/(y+c)>x/y? 1) y>

by Max@Math Revolution » Thu Feb 25, 2016 5:15 pm
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.
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by Brent@GMATPrepNow » Thu Feb 25, 2016 6:21 pm
Max@Math Revolution wrote: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- ... cy?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
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Feb 28, 2016 4:46 pm
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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