If x and y are positive numbers, is

jjjinapinch wrote:If x and y are positive numbers, is (x+1)/(y+1) > x/y?

(1) x > 1
(2) x < y

Official Guide question
Answer: B

Target question: Is (x + 1)/(y + 1) > x/y ?

Given: x and y are positive numbers
This is a great candidate for rephrasing the target question
We have the inequality: (x + 1)/(y + 1) > x/y
Since y is positive, we can multiply both sides of the inequality by y
Likewise, since y is positive, we know that y+1 is positive, which means we can multiply both sides of the inequality by (y+1)
When perform both of these multiplications we get: (x + 1)(y) > (x)(y + 1)
Expand to get: xy + y > xy + x
Subtract xy from both sides to get: y > x
So, we can now ask...
REPHRASED target question: Is y > x ?

Statement 1: x > 1
There's no information about y, so there's no way to determine whether or not y > x
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x < y
Perfect!!!
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Hi All,

We're told that X and Y are POSITIVE numbers. We're asked if (X+1)/(Y+1) is greater than X/Y. This is a YES/NO question can be solved with a mix of TESTing VALUES and a rarer Number Property rule.

1) X > 1

IF....
X = 2 and Y=1, then we have 3/2 vs. 2/1 and the answer to the question is NO.
X = 2 and Y=3, then we have 3/4 vs. 2/3 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) X < Y

Since X and Y are both POSITIVE, we actually have a rare Number Property rule that we can take advantage of. When dealing with a POSITIVE fraction (meaning a fraction between 0 and 1), adding 1 to both the numerator and denominator will ALWAYS make the resulting fraction BIGGER. For example:
2/3 becomes 3/4 and 3/4 is BIGGER
3/7 becomes 4/8 and 4/8 is BIGGER
1/4 becomes 2/5 and 2/5 is BIGGER
Etc.

Fact 2 tells us that X < Y, so X/Y will be a positive fraction less than 1 and (X+1)/(Y+1) will ALWAYS be greater than X/Y. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich