akhilsuhag wrote:If x and y are positive integers, is (x/y)<(x+5)/(y+5) ?
Statement #1: y = 5
Statement #2: x > y
Given: x and y are positive integers
Target question: Is x/y < (x+5)/(y+5)?
This is a good candidate for
rephrasing the target question.
Since y is POSITIVE, we can safely take the inequality
x/y < (x+5)/(y+5) and multiply both sides by y.
When we do this, we get:
x < (y)(x+5)/(y+5)
Also, since y is POSITIVE, we also know that (y + 5) is POSITIVE
So, let's take the inequality
x < (y)(x+5)/(y+5) and multiply both sides by (y + 5).
We get:
(x)(y+5) < (y)(x+5)
Expand both sides to get:
xy + 5x < xy + 5y
Subtract xy from both sides to get:
5x < 5y
Divide both sides by 5 to get:
x < y
We now have a very simple, REPHRASED target question. . . . .
REPHRASED target question: Is x < y?
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: y = 5
Since we have no information about x, there's no way to determine whether
x < y
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > y
Perfect.
With information, we know (with certainty) that the answer to the REPHRASED target question is
NO, x is NOT less than y
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
