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

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If x and y are positive numbers, is \(\frac{x + 1}{y + 1} > \frac{x}{y}\)?

x & y are POSITIVE numbers

\(\frac{x + 1}{y + 1} > \frac{x}{y}\)

Lets simplify the equation, as we are given that x & y are positive integers we can multiply the R.H.S. with the L.H.S. as there will not be any impact on the inequality SIGN of the equation.

\((x + 1) * (y) > (y + 1) * (x)\)

\(xy + y > xy + x\)

Cancelling \(xy\) from both the sides.

\(y > x\)

So we want to answer, Is \(y > x\) ?

(1) \(x > 1\)

This does not tell us anything about y. Hence, Eq. (1) =====> NOT SUFFICIENT

(2) \(x < y\)

We can write it as y > x, this is what we have to prove. Hence, Eq. (2) =====> SUFFICIENT

Hence, Answer is B

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x+1/y+1>x/y
cross multiply
xy +y > xy + x
subtract xy from both sides
y > x or x<y?

Ans B.

Sent from my SM-G935F using GMAT Club Forum mobile app

Might as well share that I picked C due to not Reading that x and y - positive. This would not allow crossmultiplication.

Posted from my mobile device

x and y are positive numbers
\(x,y>0 ;
(x+1)y>(y+1)x ;
y>x\)

(1) x > 1
X can be a proper fraction or improper fraction and y can be proper or improper fraction
NS
(2) x < y
Rephrased expression
Suff

Option B
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We are given that x and y are positive numbers and need to determine whether (x + 1)/(y + 1) > x/y. Simplifying the question, we have:

Is y(x + 1) > x(y + 1)? (Note that we multiplied each side by y(y + 1), which is allowed because y > 0.)

Is yx + y > xy + x?

Is y > x?

Statement One Alone:

x > 1

Since we do not know anything about y, statement one alone is not sufficient to answer the question.

Statement Two Alone:

x < y

We see that statement two has answered the question; y is greater than x.

Answer: B
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(1) x <1 -- Insufficient
(2) x< y
let's understand:

Effects of addition
if the ratio is less than 1: After adding some positive number to the numerator and denominator, the resulting ration increases
eg 2/3
adding 10 to numerator and denominator
2+10 / 3+10 =12/13 > 2/3

if the ratio is greater than 1: After adding some positive number to the numerator and denominator, the resulting ration decreases eg. 7/5
7+20 /5 +20 = 27/25 <75

Hence B is correct

please correct me if I am wrong

Here, x and y are positive numbers (i.e., \(x>0\) and \(y>0\))
If this is the case then \(\frac{x}{y}\) must be positive. If \(\frac{x}{y}\) is positive, then \(\frac{x + 1}{y + 1}\) must be positive too..
So, the question is:
\(\frac{x + 1}{y + 1} > \frac{x}{y}\)?
I can answer this question if I know value of x and y (whatever the value it is!).

In statement 2:
Here is given that \(x < y\).
I don't care what about the specific value of x and y here. I know from this statement that y is greater than x. If the statement even says that x is greater than y, i still don't care because statement NEVER lies!. Without any calculation in statement 2, I can surely say that it gives a definite YES or a definite NO, but NOT the simultaneous YES and NO. So, sufficient.


In statement 1:
There is no value of y. So, insufficient.
Is my understanding wrong Bunuel, IanStewart?
Thanks__

It might be a silly question, but before ruling Statement 1 out, can't we use the fee values of Y (as the question stem says Y is a positive number) ?
Use few positive values of Y and plug in the question to see if we get all Yes or all No?

cross multiply the given expression,
y(x+1)>x(y+1)
xy+y>xy+x
y>x ???

a. x>1. no info on Y. Not sufficient (Cancel AD)
b. y>x. Sufficient.
Answer B