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

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

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

You liked the solution, 1 Kudos Please!
_________________

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

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
_________________

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__
_________________